The US president said the first tranche, comprising 300,000 tons, would be released immediately in a post on his own social network, Truth Social.
He said it would be followed by another 500,000 tons in November, with a further one million tons "immediately thereafter".
Russia would then provide three million tons "within a short period of time", he added.
A US ton equates to 907kg, while a metric tonne weighs 1,000kg.
Mr Trump went on to say that "Lower prices for Americans, especially our Great Farmers, Ranchers, and Truckers, is my Greatest Priority".
In the aftermath of the announcement, he told reporters in Washington: "That is massive amounts of oil coming into our country, and I want to thank President Putin to be honest with you."
Ukrainian President Volodymyr Zelenskyy criticised the agreement, characterising it as a "gift to Putin".
He said the Russian leader is "relying on attempts to strike backroom deals to secure some form of pressure relief for Russia".
Mr Zelenskyy added: "Any easing of sanctions against Russia without a clear and lasting de-escalation agreement... is an obvious weakness.
"It plays into Russia's hands - allowing it to kill more, wage war for longer, have even less respect for America, and inflict even greater losses and damage on the world."
Responding to the announcement, the UK pledged to "maintain pressure on Russia" through the "toughest sanctions regime" it had ever imposed.
A UK government spokesperson said: "We will continue working closely with international partners to ensure Ukraine has the military and financial support it needs to defend itself.
"We will also maintain pressure on Russia through the toughest sanctions regime ever imposed by the UK, increasing the cost of Putin's aggression and supporting efforts to secure a just and lasting peace."
Mr Putin said it would have a "positive impact on the entire global economy" in a statement issued by the Kremlin.
His phone call with the US president - initially expected to focus on the suspected plague death in Siberia - also covered the war in Iran and prospects for resolving the "Ukrainian crisis", the statement added.
Russia's deputy prime minister Alexander Novak said his country was ready to start supplying diesel to the US and other countries in October, with exports set to increase in November and December.
The Treasury Department said it would immediately issue a temporary license allowing Russian diesel to be supplied to the global market following Mr Trump's announcement.
The US has not imported Russian oil or gas since 2022, when then-president Joe Biden banned them following Moscow's invasion of Ukraine.
Fuel prices have risen dramatically since the start of the US-Iran war and remain high as America prepares to head to the polls for the midterm elections on 3 November.
The national average for a gallon of diesel in the US was $6.23 (£4.71) on Friday after hitting a record $6.52 (£4.92) on 22 September.
Mr Trump has recently pressured G7 allies to release emergency reserves and expanded access to tax-exempt red-dyed diesel, which is typically reserved for farm equipment.
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Last month, he signed a sanctions law targeted at Russia's energy economy and other areas which fuel its war against Ukraine.
It applies to Russian officials, banks, and a shadow fleet of tankers.
The measures also ban all new US investment in Russia and the handling of sovereign debt.
The parade has led to a stand-off between Orangemen and nationalist residents of the Garvaghy Road in Portadown lasting almost two weeks.
Sir Chris said he had been "trying to find a solution to that stand-off" having heard "both sides of the argument", but "unfortunately, we've not been able to do that".
The Parades Commission ruled two weeks ago that the march could pass along the Garvaghy Road with restrictions in place.
But the parade, from Drumcree Church into Portadown, did not happen because of a large protest on the road.
Sinn Féin leaders Mary Lou McDonald and Michelle O'Neill have said there is an "enormous sense of relief" on the Garvaghy Road in Portadown after the announcement that the Parades Commission determination to allow the Drumcree parade has been overturned.
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Sir Chris said in a statement: "I have spent the last fortnight trying to get a mutually acceptable agreement between the two sides, hosting several rounds of negotiations at Hillsborough Castle last week and maintaining frequent contact with both sides since then.
"Unfortunately it has not been possible to achieve a local resolution. I have therefore been intensively considering all options for bringing this dispute to an end."
He added: "Consequently, and in the interests of wider public interest and safety, I've come to the conclusion that the circumstances under which that decision was made have now changed considerably.
"As a result, the procession cannot go ahead as it was determined. I have not taken this decision lightly."
Asked if he was worried he had surrendered to lawlessness and rewarded those who blocked the road in Portadown, Sir Chris said: "I warmly commend everybody at the Portadown Lodge for the way that they've co-operated with the police over the last fortnight and for that matter cooperated with me and spoken very openly about their concerns and the way they would like to be able to accommodate others."
DUP leader Gavin Robinson said Sir Chris needs to "explain what his Government intends to do to restore confidence in the rule of law".
The plan was inspired by the 9/11 attacks, UAE attorney general Hamad Saif al Shamsi said, and the suspect had used two previous flights to Tel Aviv to survey the route and the airport.
On the day of the hijacking, he allegedly attacked captain Smit Machchhar with a crash axe, typically kept in the cockpit for use during emergencies.
The plane was carrying more than 170 passengers and crew, most of them Israeli - and plunged 16,000 feet in 30 seconds during the incident.
The suspect - identified as Omani national Hamam al Hammami - was co-pilot aboard flight FZ1073 from Dubai to Tel Aviv on 30 September.
Mr Machchhar was hailed a hero after he managed to open the cockpit door, despite being wounded.
Passengers and crew were able to subdue the alleged attacker and relief pilots safely landed the plane in Saudi Arabia, where the suspect was later transferred to the UAE on Thursday.
He worked for several airlines in different countries, including Oman Air, before joining flydubai in January 2026, the attorney general said.
He added that the suspect had met all professional and security requirements, but "none of the procedures revealed any indications of his extremist views or his intention to carry out a terrorist plot".
Sources earlier told the Associated Press that al Hammami - who has a Syrian mother and was born in the UAE - was banned from flying by Oman over fears he had adopted extremist views.
Earlier this week, Israeli prime minister Benjamin Netanyahu said pilots who are citizens of countries that Israel does not have diplomatic relations with, including Oman, are not permitted to operate flights to the country.
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He also claimed that the co-pilot had undergone "Islamist radical indoctrination" and said it appeared "very likely that he was going to down the plane".
New Zealand Assistant Police Commissioner Michael Johnson said on Monday that the co-pilot had spent time in the country, with police looking into the period.
An Australian counterterrorism unit is also investigating his links to Australia, while Buckinghamshire New University in the UK has confirmed he completed a distance-learning course in aviation management.
It is being classed as a category three - the third highest - and is expected to result in a "life-threatening" storm surge, "extremely dangerous and damaging" winds, flooding and possibly tornadoes.
Residents along the US Gulf Coast have been boarding up windows, laying sandbags and getting last-minute supplies in preparation for the storm, which is the first in an unusually quiet hurricane season.
The last one to hit the eastern US was Milton, which struck the Gulf Coast of Florida in 2024.
Isaias is due to come ashore between Mobile Bay on the Alabama coast and the city of Destin in the Florida Panhandle - an area known for white sandy beaches, holiday homes and waterfront bars.
The National Hurricane Centre said a "life-threatening" storm surge, which could be 1.8m-2.7m (6ft-9ft), was expected from the mouth of the Mississippi River to Suwannee in Florida.
And "extremely dangerous" hurricane-force winds were anticipated over parts of the Florida Panhandle, southern Alabama and southern Mississippi, where a hurricane warning is in effect.
On Friday morning, it packed 120mph (193kph) sustained winds and was picking up speed.
"Damaging wind gusts were likely over a large portion of the southeastern US from western and northern Georgia westward over much of central and northern Alabama, southern middle Tennessee and Mississippi," the centre said.
It added: "Isaias will bring areas of heavy rainfall to the central US Gulf coast and much of the southeast throughout the weekend."
Alabama governor Kay Ivey has ordered non-residents to evacuate Gulf Shores, Orange Beach and Dauphin Island.
And Florida governor Ron DeSantis has warned people to expect floods, wind damage, power outages and fuel shortages.
"When the water's rising and things are happening, it's a very, very difficult conundrum and you do not want to be caught in that," he said.
But Anne Petzold, who lives with her husband in the Florida beach community of Gulf Breeze, said they and all of their neighbours plan to ride out the storm.
The couple have put up hurricane shutters, removed anything in their yard that could become a projectile and have two generators ready if they lose power.
"Everybody does what they can do, everybody asks if they need help - they ask for help, they offer help. All good," she said. "It's just another adventure."
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Once it comes ashore, Isaias is expected to weaken until it is downgraded to a tropical storm by Saturday afternoon.
But heavy rain is still forecast as it moves inland, with 10-20cm (4-8in) or more expected through the weekend.
On the day he was due to go to trial earlier this week, David Barraclough, 46, admitted to murdering Carolann Barraclough, 37.
She was found dead at her house in Horbury, Wakefield, after police responded to a concern for safety report in March.
Judge Andrew Stubbs KC described her murder as "a brutal attack with a hammer whilst she lay in bed" and noted that her three children were present in the home at the time.
He said Mrs Barraclough was then placed in the utility room freezer wrapped in a duvet, with her hands and ankles bound with tape, and a bin liner over her head.
He added that it was "merciful" that the children did not witness the attack or find their mother's body in the two weeks it remained concealed.
At Leeds Crown Court on Friday, Barraclough was jailed for life, with a minimum term of 22 years and one month.
He refused to appear for sentencing, and Judge Stubbs said he wanted to use new legislation to force his attendance, backed with the threat of a two-year jail sentence, but the powers are not yet in force.
Addressing the absent Barraclough, he said: "Thereafter, your behaviour displayed a callous disregard for your wife, her children, your children and her friends".
He continued: "As your wife lay dead and undiscovered in the freezer, contrary to your subsequent claims to be heartbroken, you joined dating apps, contacted escorts and exchanged explicit messages with another woman.
"You used your wife's bank card for your joint account to withdraw large amounts of money to support the life you were living."
The court also heard that he used Mrs Barraclough's phone to convince her daughter that she was exchanging messages with her mother in hospital.
On 2 March, he sent a message to her eldest child, saying: "I'm starting to feel a bit better I'll be home soon".
And on 4 March, he sent "love you have a good day".
The court heard that Barraclough turned himself in at a police station on 5 March, saying he killed his wife on 20 February and claiming to be a victim of domestic violence.
But Judge Stubbs said his account was "riddled with lies" and that he had subjected Mrs Barraclough to years of violence and controlling behaviour.
He noted that the day Barraclough walked into the police station, the couple had 16p left in their accounts.
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In a statement read to the court, Mrs Barraclough's sister, Sarah Rowley, described how the whole family were "completely shattered by the senseless and violent way Caz was taken from us".
She said her children were the "centre of her world" and added: "The void of her absence is agonisingly loud."
Jill May, senior crown prosecutor for Crown Prosecution Service Yorkshire and Humberside, said: "David Barraclough tried to paint himself as a victim of domestic abuse who had no choice but to kill his wife and was heartbroken by what had happened. The evidence told a very different story.
"His actions in the weeks after her death, including downloading dating apps and taking out large sums of money from their joint account, were blatantly not those of a man in mourning."