They were immediately transferred to two Sea King helicopters, which flew them to the Chivenor Royal Marine barracks in Devon to be debriefed.
There the crew disembarked at about 14:30 BST in an orderly fashion and were greeted by a row of officials before being led inside to be reunited with their waiting families.
A joint statement from the 15 Royal Navy personnel said: "It goes without saying that we are all extremely happy to be back home in the UK and reunited with our loved ones. Touching down at Heathrow this morning was, for all of us, a dream come true, and the welcome home we have enjoyed today is one none of us will forget.
"The past two weeks have been very difficult. But by staying together as a team we kept our spirits up, drawing great comfort from the knowledge that our loved ones would be waiting for us on our return to the UK," the statement continued.
"It is only now that we have learnt of the enormous public support we have all enjoyed in the UK, and wish to thank everyone for their thoughts, kind words and prayers. It means so much to us all."
The sailors' ordeal began 13 days ago on March 23rd when the crew were seized by Iranian forces in waters close to the dividing line between territorial waters controlled by Iran and Iraq.
It ended yesterday when Iranian president Mahmoud Ahmadinejad unexpectedly announced that he would pardon the service personnel as a "gift" to the British people.
Britain's ambassador to Iran was subsequently given access to the hostages for the first time since their capture following the theatrical press conference given in Tehran by Mr Ahmadinejad.
Despite agreeing to release the sailors, the Iranian president attacked Tony Blair's government for refusing to "admit it had made a mistake" by continuing to insist that the crew were in Iraqi waters, working under a United Nations mandate, when they were seized by Iranian forces in the Gulf on March 23rd.
Today the prime minister reiterated his government's position that the British vessel had not strayed from Iraqi waters.
The 15 sailors, who were released to the British embassy in Iran some hours after Mr Ahmadinejad's announcement, were earlier shown on television shaking hands with the Iranian president following his statement and apparently thanking him for freeing them.
Commenting on today's events, First Sea Lord Admiral Sir Jonathon Band said he was delighted to welcome the sailors back to the UK.
"While I am naturally extremely pleased that this unfortunate situation has been resolved peacefully and diplomatically, I would like to offer my condolences and sympathy to the families of those who have given their lives on operations and have not been able to enjoy the type of homecoming we see today.
"I think in particular of the families of the two sailors killed in HMS Tireless recently and the families of the six soldiers who have died in Iraq in the last week," he added.
The Ministry of Defence has also for the first time confirmed the names of the 15 personnel involved in the dispute. They are:
Captain Christopher Air
Lieutenant Felix Carman
Chief Petty Officer Gavin Cavendish
Acting Sergeant Dean Harris
Leading Seaman Christopher Coe
Acting Leading Seaman Faye Turney
Lance Corporal Mark Banks
Marine Paul Barton
Able Seaman Andrew Henderson
Marine Adam Sperry
Marine Joe Tindell
Marine Daniel Masterton
Able Seaman Simon Massey
Able Seaman Arthur Batchelor
Able Seaman Nathan Summers
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