The 15 Royal Navy crew members held captive by Iran are flying home after being freed by President Mahmoud Ahmadinejad as a "gift" to the UK.
The crew are in good health, according to the Foreign Office
They are due to land at Heathrow at 1200 BST and will later be reunited with relatives at a military base.
Before leaving Tehran, several of the crew spoke on Iranian television to express thanks for their release.
Prime Minister Tony Blair said the homecoming would be "a profound relief" to the personnel and their families.
'Firm but calm'
The navy personnel arrived at Tehran Airport in a fleet of official cars, after 13 days in Iranian custody.
They left at about 0800 local time (0530 BST) on a British Airways flight bound for London.
Military officials say they will be flown by helicopter to Royal Marines Barracks Chivenor in Devon, where they will be de-briefed and reunited with their families.
Before leaving, one of the 15, Lt Felix Carman, told Iranian television: "To the Iranian people, I can understand why you were insulted by our apparent intrusion into your waters.
"I'd like to say that no harm was meant to Iranian people or its territories whatsoever, and that I hope that this experience will help to build the relationship between our countries."
The only woman in the group, Leading Seaman Faye Turney, said: "Apologies for our actions, but many thanks for having it in your hearts to let us go free."
Both said they had been well treated by their captors.
Mr Ahmadinejad said no concessions had been made by the British government to secure the releases, but that Britain had pledged "that the incident would not be repeated".
Prime Minister Tony Blair said Britain's approach to the crisis had been "firm but calm - not negotiating but not confronting either".
'Blaze of publicity'
Speaking at a news conference, Mr Ahmadinejad repeated Iran's view that the crew had "invaded" Iranian waters but said they were being freed as a "gift" to the British people.
Britain says the crew were in Iraqi waters under a UN mandate when they were captured, and says the confessions were extracted under duress.
Former British ambassador to Iran Sir Richard Dalton said Iran's reputation had been harmed by the episode.
"I think Iran's reputation has deteriorated where it counts, in many capitals, including the capitals of countries which are close to it who have joined in the effort to get these captives released," he said.
"The action which the Iranian government has taken gives them a blaze of favourable publicity which is going to be short-lived, and it's not going to alter the difficulty of addressing these major issues, like the nuclear question, and is not going to give Iran any leverage in them."
However, former US ambassador to the United Nations John Bolton said President Ahmadinejad was the clear winner and had been strengthened in his pursuit of nuclear weapons.
"President Ahmadinejad comes out of this as a winner on two counts," he said.
CAPTURED NAVY PERSONNEL
Chris Air, 25, from Altrincham in Cheshire
Mark Banks, 24, of Lowestoft, Suffolk
Paul Barton, of Southport, Merseyside
Arthur Batchelor, 20, of Plymouth
Felix Carman, 26, of Swansea
Christopher Coe, 31, of Huddersfield
Dean Harris, 24, of Carmarthen, west Wales
Danny Masterton, 26, of Muirkirk, Ayrshire
Adam Sperry, 22, of Wigston, near Leicester
Nathan Summers, of Hayle, Cornwall
Joe Tindell, 21, of south London
Faye Turney, 26, originally from Shropshire
One captive remains unnamed
"He won by seizing British hostages and he won by unilaterally deciding to release them, having found out the answer to the question I think he was posing, which is - how strong a response will Britain make to this act of taking captive these 15 service members?
"The reaction was - not much at all. I think Ahmadinejad is actually emboldened in his pursuit of nuclear weapons, and I think that means more trouble ahead for all of us."
And the father of one of the crew members criticised Tony Blair's handling of the crisis.
Paul Carman, the father of Lt Carman, said: "I've been very disappointed and in some cases extremely angered by what I regard as risible attempts at bravado, absolutely ridiculous schoolboy diplomacy."
Jimmy Carter, who was US President in 1979 when American nationals were taken hostage at the US embassy in Tehran, said he was impressed that diplomacy had solved the crisis.
"As soon as the harsh rhetoric was assuaged on both sides - from London and also from Tehran - then normal diplomacy prevailed. I'm very grateful to see that," he said.
Former Chancellor Lord Lamont, who is president of the British-Iranian Chamber of Commerce, said he believed the government made a "big mistake" by going to the UN.
"It clearly irritated the Iranians hugely - they didn't want this international involvement and things went much better when it was handled diplomatically, one country to one country."
The BBC's Frances Harrison in Tehran said speculation was likely to continue over whether the release had anything to do with developments in Iraq.
There, an Iranian envoy has reportedly been given access to five Iranians captured by US forces and a kidnapped diplomat was released on Tuesday.