The US rapper challenged Robert Kraft, who did not allow him to perform at his Gillette Stadium in Massachusetts as part of The Loop tour, to match his donation.
He has now responded by saying that he and Sheeran have pledged $2m (£1.5m) each "to aid in the region".
It comes after Macklemore said he had been removed as Sheeran's opening act over pro-Palestine comments he made during a show in New Jersey.
All the other artists scheduled to perform as part of the tour - including Danish band Lukas Graham and Billie Eilish's brother and musical collaborator, Finneas - subsequently pulled out in protest.
In a statement posted on social media, Macklemore wrote: "With everything that has happened over the last 48 hours, I want to bring the conversation back to where it belongs: to the Palestinian people who are still being killed, still living under military occupation, and still fighting for their freedom.
"I will be donating the entire $1 million of my net earnings from Ed Sheeran's Loop Tour to six organizations working directly to support the Palestinian people. And I invite Robert Kraft to match my donation. Whatever we disagree about, perhaps we can agree on this: Palestinian lives are worth protecting. A Palestinian life is no less valuable than any other life on this earth."
Mr Kraft, the owner of the New England Patriots, said in an Instagram post shortly after Macklemore's statement that he and Sheeran would pledge the money "to aid in the region to fight this humanitarian crisis", although he did not specify which organisations or charities would receive the money.
"I have dedicated much of my life to building bridges between all people. I believe deeply that all lives are worth protecting," Mr Kraft said.
"Ed now plans to reach out to other venue owners and our goal is to continue to work together to build bridges," he added.
Earlier this week, Sheeran said he was "appalled by the conflict between Israel and Palestine", and described the "suffering and pain caused on both sides" as a human tragedy in a lengthy Instagram statement.
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"I am not complicit," he said. "I have my personal views on this devastating conflict. Just because I choose not to speak publicly, it doesn't mean I don't have them, and it doesn't mean I don't care."
Sheeran also said that "Macklemore coming off tour was the promoter's decision, it was not mine", adding that the rapper's contract for the tour "was with the promoter, not me".
In a statement provided to Sky News' US partner network NBC News, Mr Kraft had said the decision on his venues was reached following Macklemore's comments and "a broader history of antisemitic rhetoric and imagery that we believe has been deeply offensive and hurtful to the Jewish community".
He said: "This decision is not about diminishing the suffering of innocent Palestinians or denying anyone the right to advocate on their behalf. Their pain and loss are real."
The book claims in the days after the death of Diana, Princess of Wales, then-Prince Charles told her brother "rest assured, we'll forget her soon enough".
The comment was allegedly made during the arrangements for Diana's funeral where Prince William and Prince Harry, then aged 15 and 12, would walk in their mother's funeral procession in September 1997.
In response to the claims, a Buckingham Palace spokesman said Charles is "mindful that the pain of fraternal grief can cloud reason".
"While we do not comment on books as a matter of principle, His Majesty is mindful that the pain of fraternal grief can cloud reason, affect judgment and colour memory in ways others do not recognise, even many years after such a loss," the statement adds.
The allegations were made in the book Swan Song: Diana, My Sister, which is being serialised in the Daily Mail - and is due to be published next week.
The book also claims the Earl insisted Diana would not have wanted her young sons to have made the difficult public walk.
Sky News' royal correspondent Laura Bundock described the statement from Buckingham Palace as a "really remarkable intervention" and a "very robust response" which is "beyond punchy".
"It is, as they say very unusual for them to make any comment about a book. They normally do not comment on books," she added.
Bundock noted Buckingham Palace didn't respond to Prince Harry's book Spare.
"This is a very different situation, [I think] at this point they feel they simply cannot stay silent given who has written the book, Diana's brother, given the subject of the book, Diana herself, and given the nature of the allegations made," Bundock added.
Princess Diana died in a Paris car crash in August 1997.
William, Harry, Charles, Prince Philip and the Earl walked behind Diana's coffin in a funeral procession through central London to the funeral service at Westminster Abbey.
Noah, who was autistic, non-verbal and partially deaf, went missing on Tuesday afternoon after he ran down an alleyway during a visit to a village playground in Brantham.
The boy became separated from a relative and his disappearance sparked a major search operation involving the police, coastguard and about 1,300 volunteers.
:: How the Suffolk search unfolded
On Wednesday, Superintendent Tom Pearse said a child's body had been discovered in a nearby pond.
"Formal identification has yet to take place, but the family of Noah Woods have been informed of this development," he said.
"The discovery of the body is currently being treated as not suspicious but unexplained."
The body was recovered from Decoy Pond, a fishing lake near to the play area in Merriam Close where he was last seen.
Specialist dive teams from the Metropolitan Police had been deployed to assist with the hunt for the boy and were seen searching the water on Wednesday afternoon.
The search was made more difficult because Noah would not have responded to his name if called.
As well as a massive ground search, helicopters, sniffer dogs, thermal imaging were used to try and find Noah, with police going door to door and scouring CCTV.
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Superintendent Pearse, who was visibly emotional, said police had been "overwhelmed by the outpouring public support" and the number of volunteers "putting on their boots and helping us search".
"As a parent myself, I completely understand why people would want to help and such a response is one that typifies the strong sense of community and the heart-warming nature of Suffolk people that make the county such a special place," he said.
"I am sure you appreciate the family now need time, space and privacy and I thank you for your understanding in this."
Volunteers who were gathered in a garden area at Brantham Leisure Centre were brought to tears after Mr Pearse broke the news.
Brantham Parish Council said: "Our thoughts are with Noah's family, friends and everyone who knows and loves him at this incredibly difficult time."
The leisure centre, which had become a hub for search efforts and the massive community response, will remain open on Thursday to offer support, the council said.
Police released CCTV shortly after midday on Wednesday showing Noah's last known movements at the playground.
The footage shows him running and interacting with a piece of play equipment.
Rescuers had pulled 82 bodies out of the al-Zara mine in Nuhud, a town in West Kordofan province, by Wednesday afternoon, unnamed local officials said.
The area is controlled by the paramilitary Rapid Support Forces (RSF), which has been fighting against the Sudanese military for more than three years.
Dozens of people remain unaccounted for, according to Suleiman Abu Hmeida from Emergency Response Rooms, a grassroots network.
The network monitors the conflict and provides support for communities across the conflict-ravaged country.
A lack of equipment is hampering rescue efforts, the official said, with only one privately-owned forklift truck in use.
Khairal-Sayed Gabara, one of the survivors, said the collapse was "massive", adding that the situation was "very dire".
"We do not have the machinery to lift dirt and stones and search for survivors at depths of more than 30 metres [100ft]," he said. "There were dozens of people working in the mine."
Al-Amin Suliman, another survivor, said 60 bodies had been recovered as of Wednesday morning, but "there are still people stuck inside".
The collapse, which started on Sunday in one of the mine shafts and spread to the other interconnected shafts, happened at one of thousands of small-scale mines scattered across Sudan.
The al-Zara mine - an informal site that employs unregulated workers - lacked basic safety and protective measures, according to the Sudan Doctors Network, a medical group tracking the war in Sudan.
The Kordofan Observatory monitoring group said the mine lies on a half-mile (1km) site on an area of fragile, sandy soil.
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Despite being a major gold producer, deadly mine collapses are not uncommon in Sudan, where safety standards are not widely applied.
Similar disasters in 2021 and 2023 killed a total of 52 people.
At least 59,000 people have died in the conflict between the RSF and the country's military, according to Armed Conflict Location & Event Data, a monitoring group.
Parts of Sudan have been pushed into famine.
Large quantities of gold have been smuggled out of the country to finance the RSF, which controls gold-producing areas in the Darfur and Kordofan regions, according to experts commissioned by the United Nations.
The Premier League club announced the transition on Wednesday, with the US private equity firm acquiring "full control of the club".
In a statement, Mr Boehly, who bought a stake in the London club in 2022, said it had been an "honour" to serve as chairman, and thanked "the coaches and players, the talented leadership and staff at Chelsea, and the legions of dedicated fans".
He added: "I have valued my partnership with Clearlake and the wider ownership group, and the collective decisions and investment we have made to support the immediate and long-term success of the club. I am confident that Chelsea is well positioned for continued success under Clearlake's leadership."
Mark Walter, another of the club's co-owners, has also sold his stake to Clearlake. Last month, he sold NBA franchise the Los Angeles Lakers for a record-breaking $12.5bn (£9.25bn).
Mr Boehly, Mr Walter and Swiss billionaire Hansjörg Wyss - who the club said will remain an "important stakeholder and partner in the ownership group" - each had a 12.8% stake following their joint takeover of Chelsea four years ago, with Clearlake previously owning 61.5% as part of the deal.
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Following the acquisition of the club from former owner Roman Abramovich, who was forced to sell after being sanctioned by the UK, Mr Boehly became the public face of the club, overseeing a period of intense activity in the transfer market that saw Chelsea spend more than £1bn.
In July, Chelsea broke the record for the most expensive transfer for a British player when they signed England international Morgan Rogers from Aston Villa for £117m.
Behdad Eghbali and Jose E Feliciano, co-founders of Clearlake, said Mr Boehly had been "an important partner throughout our ownership", and insisted the 52-year-old "will always be a part of the Chelsea story and family".
Chelsea, who appointed Xabi Alonso as manager this summer and are currently sixth in the Premier League, said there will be "no changes to day-to-day operations, leadership or strategy at the club".