The body of Elisabeth-Jane Ross, 38, was discovered by a homeless man in a derelict building in the Kypseli area of the Greek capital on 18 July.
Ms Ross, from the Edinburgh area of Scotland, is believed to have died between five and seven days before she was found, police said.
It is understood she arrived in the country from the United States via Cyprus on 29 June, according to Greek media.
She was initially staying with friends in Piraeus and is then said to have gone to meet American friends in another part of Athens, but it is unclear if this ever happened.
Earlier this week, toxicology tests were being carried out to establish whether "foul play" was involved in her death.
The Hellenic Police, Greece's national force, were able to identify the victim using fingerprints.
In the following days after her death, police said her bank card was still being used to withdraw money and text messages were being sent from her phone.
On Sunday, Greek police said a 26-year-old man, described as a foreign national, has been arrested on suspicion of manslaughter, robbery and violation of weapons laws.
A replica pistol and a knife were allegedly found at the suspect's home.
Read more:
Helicopters collide tackling Greek wildfires
'One punch' killer to be extradited to Greece
Great-grandfather died after garden crash
The Foreign and Commonwealth Office (FCO) said earlier it was "providing consular support and are in contact with the local authorities".
A Police Scotland spokesperson said: "We are aware of the death of a Scottish woman in Athens and are liaising with authorities in Greece.
"Officers are providing support to her family in Scotland."
The victim, who was in his 30s, died at the scene in Calcutt near Cricklade on Sunday morning.
Officers said a murder investigation has now been launched and "urgent enquiries" were taking place to "establish the full circumstances of the incident".
A man in his 70s and a woman in her 40s have been arrested on suspicion of possession of a firearm and assisting an offender.
They have been taken into custody for questioning by detectives.
Wiltshire Police said that around 8.15am officers received a report from paramedics that a man had been shot at a Traveller site.
The force said emergency services went to the scene where the man was pronounced dead.
An area around the scene has been cordoned off, and there is still a "significant policing presence" while an investigation is carried out.
Officers have contacted the victim's loved ones, the force said.
Detective Chief Inspector Phil Walker, from the major crime investigation team of Wiltshire Police, said: "This is an incredibly serious incident, and my thoughts are with the victim's friends and family at this devastating time."
He added: "Enquiries are ongoing at the site and in the wider area to establish the circumstances which have led to this incident and locate all the people involved.
"A cordon is in place at the site and the road leading to it has been closed to allow for enquiries to be conducted and I would ask that this is respected.
Read more from Sky News:
Man arrested after Briton's body found in suitcase
At least five killed after ferry catches fire
"Those in the area will see an increased policing presence throughout the evening as enquiries continue."
Wiltshire Police are appealing for anyone who has "any information or witnessed anything suspicious this morning" to contact officers or call Crimestoppers anonymously.
Police said emergency services were called to the festival site in the Lake District in Cumbria at 2.13am, following reports of the girl suffering a "medical episode".
Despite the best efforts of emergency responders, including the administration of CPR, she was pronounced dead at the scene, Cumbria Constabulary said.
The girl's family have been told and are being supported by specialist officers.
Enquiries into the circumstances surrounding her death are ongoing.
Police are keen to speak to people who were in the area of the festival's Calling Out tent and the Big Wheel at around 2am.
They also want to speak to a group of women who directed emergency personnel to the girl after becoming concerned for her welfare.
A festival spokesperson said in a statement: "The team at Kendal Calling are deeply saddened by the passing of a festival attendee in the early hours of Sunday morning following a medical episode.
"As soon as the individual became unwell, they were immediately attended to by our on-site security and medical teams.
"Paramedics and medical personnel provided emergency care at the scene and did everything they could to help.
"We extend our deepest sympathies to the individual's family, friends and loved ones at this incredibly difficult time.
"We are supporting the relevant authorities and will continue to assist them with their investigation."
The four-day festival, which continues Sunday (2 August), is being headlined by acts Biffy Clyro, Wolf Alice, Two Door Cinema Club and The Kooks.
Growing year on year since its launch in 2006, Kendal Calling takes place annually at Lowther Deer Park, near Penrith and Hackthorpe.
This story contains details some readers may find distressing.
Harrison Simpson, 22, and the toddler's mother, 26-year-old Alexandra Walker, were jailed last week for murdering Isabelle Welsh after weeks of abuse.
Isabelle collapsed at her home in September last year following a "massive head injury". A post-mortem found she suffered 21 broken bones in the weeks leading up to her "sadistic" death.
Cleveland Police has told Sky News that Simpson was charged with breaching a non-molestation order in March 2024.
"A warrant for his arrest was issued that same month after he failed to appear at court," a statement said. "Multiple enquiries and arrest attempts were carried out to try to locate and arrest him but these proved unsuccessful."
Isabelle's family was told about "the circumstances surrounding the outstanding warrant early on in the investigation", the force added.
"We recognise the time Simpson had an outstanding arrest warrant is far from adequate. A review of this was immediately conducted upon his arrest for murder," the statement added, after first being reported by The Sunday Times.
Cleveland Police said several changes were made after the review, including increased visibility of outstanding warrants, a comprehensive data system to track them, and daily reviews of the highest-risk cases.
A 'sadistic' death and 21 broken bones
Simpson and Walker were convicted of murder and child cruelty, while Simpson was also found guilty of sexually assaulting the toddler.
When paramedics arrived at Walker's house in Thornaby on 13 September 2025, they found the two-year-old at the foot of the stairs without a pulse.
The trial was told that as Isabelle was dying, Walker smoked a cigarette in her kitchen and delayed ringing 999 despite Googling "why would my toddler be bleeding".
She called her stepfather to come round, and it was only on his instruction that she finally rang emergency services.
More from Sky News:
Five dead and dozens missing after ferry fire
Tourist plane crash leaves 13 dead in Peru
There were bruises all over Isabelle's body, including to her head, neck, abdomen, back and private parts. There was blood in her nappy and sick on her face, jurors were told during the trial.
Isabelle was taken to hospital but died the next day.
Prosecutor Richard Wright KC said the toddler suffered weeks of assaults and the head injury "was simply the end point in that campaign of violence".
Eleven days before her fatal collapse, Isabelle was taken to her GP and then to hospital with a broken leg.
Despite the misgivings of some staff, she was discharged after Walker claimed she must have suffered the injury after getting caught in her cot.
Walker began dating Simpson after they met on Facebook just months before - and she suspected he might be a paedophile, saying he preferred to see her with Isabelle and would bathe the toddler without her permission.
Despite being suspicious enough to check the Sex Offenders' Register, Walker did not break up with him.
Simpson refused to answer police questions or testify at trial.
The judge considered a whole life tariff for Simpson but could not be sure if the murder was sexually motivated.
Simpson and Walker were given minimum terms of 28 years and 22 years, respectively.
A high of 35C is expected by the Met Office in the South East on Monday, higher than forecasts for the Greek islands of Mykonos, Rhodes and Santorini.
Much of central and southern England is set to see highs in the upper 20s to low 30s before temperatures ease slightly later in the week.
Greece wildfires - follow helicopter crash latest
Amber alerts, the second most serious, have been issued by the UK Health Security Agency (UKHSA) for the East Midlands, East of England, South East and London regions for 48 hours from 9am on Monday.
Less severe yellow alerts are in place for the same period covering the North West, Yorkshire and The Humber, West Midlands and South West regions.
Rising temperatures bring health risks, the agency said, with greater demand for health care services by the vulnerable and an increase in risk to health for the over-65s or anyone with a pre-existing health condition.
Vulnerable at risk
Polly Ashmore, Acting Consultant in Public Health at the UKHSA, said periods of hot weather can cause "serious health outcomes, especially for older adults".
The agency is asking health and social care services in affected regions to make sure they are prepared, and reminded people "to look out for elderly relatives, neighbours, and those with underlying health conditions, making sure they are aware of the forecast and following the necessary advice".
She added: "Simple steps such as staying hydrated, avoiding the sun during the hottest part of the day, and keeping your home cool are some of the key ways to help keep yourself and others safe during periods of hot weather."
Check the weather where you are
'Incredible' UK weather
Sunday's top temperature was 31C at Frittenden in Kent.
Sky weather producer, Joanne Robinson, said Monday will see the heat "build further in the South", warning that 34C is possible in southeast England, and there is a "small chance of reaching 35C".
If the higher temperature is hit, she said "it will be the eighth day somewhere in the UK has reached 35C or more this year", something she described as "quite incredible".
Ms Robinson said it shows "just how easily extreme temperatures can be reached now".
It won't be as hot on Tuesday, but 31C or 32C but still 31 or 32C are possible in the South East, she said, adding that "it will be humid too, with some uncomfortable nights ahead".
Read more:
Scientists' fears over wildfires
UK reservoirs 'exceptionally low'
Following last week's hot and humid weather, the Met Office has said England and Wales are on course for the driest July since records began, which could be confirmed on Monday when its full, provisional data for last month is published.
This summer's prolonged dry conditions have led to wildfires breaking out across parts of the UK, including on the Suffolk coast, where a major incident was declared at Dunwich Heath, near Leiston on Wednesday and where firefighters were still on the scene on Sunday, Suffolk Fire and Rescue Service said.
Firefighters have also been tackling major fires in the Scottish Cairngorms and at Tintwistle Moor in Derbyshire.
Half of England and the whole of Wales are in drought following successive heatwaves earlier this summer.