Leading Seaman Faye Turney and her Royal Navy colleagues celebrated in Iran after Iranian President Mahmoud Ahmadinejad announced they would be released as a "gift".
The 15 service personnel from HMS Cornwall were seized on 23 March in the northern Gulf after the Iranians accused them of straying into their waters.
Members of the freed British crew were given presents by the Iranians. Lieutenant Felix Carman said he hoped the incident would help "build the relationship" between Iran and Britain.
The 14 men and one woman arrived home on a British Airways flight at the VIP section near Heathrow's Terminal Four just after 1200 BST on Thursday.
Defence Secretary Des Browne said the crew showed "immense courage and dignity" during their 13-day ordeal.
Leading Seaman Turney and Operator Maintainer Simon Massey shared a joke as they posed for photographs at Heathrow.
Iranian state television featured a short interview with Plymouth-based Leading Seaman Turney, 26, who said there was "no bad feeling at all towards Iran".
After arriving back in the UK, the crew members were taken in helicopters to a Royal Marines base in Devon where they were reunited with their families.
A spokesman for the Devonport Naval Base in Plymouth, where HMS Cornwall is based, said the crew's debrief on their return would last for "hours, not days".
The father of Leading Seaman Christopher Coe, 31, said the family was "over the moon" at his release.
The sailors and marines were finally reunited with their families at the Royal Marines Base at Chivenor, north Devon, on Thursday afternoon.