A statement from Iran's Revolutionary Guards said that after investigation it reached the conclusion that their illegal entry was a mistake.
Five British yachtsmen detained in the gulf by Iranian Revolutionary Guards have been freed. Tehran said the decision to release the men came after it found they had strayed into Iran's territorial waters accidentally.
British Foreign Secretary David Miliband says the crew have now departed Siri Island, where they were held for over a week.
"I was obviously very pleased to hear earlier this morning that the five young yachtsmen have indeed been released. I have had confirmation that they're now heading towards international waters on their way to Dubai," he said.
He says Iranian officials had dealt with the release of the five British yachtsmen in a "professional" way.
"I think that this is just a straightforward matter, it's not a political matter, I don't believe there is any wider significance of it -- it shows that diplomacy can work," he said.
David Young, father to one of the five crew, described his emotions.
"Very relieved obviously, we thought it would be over quickly and this is what we were hoping for," he said.
The five Britons were on route from Bahrain to Dubai, where they planned to take part in a 360-nautical-mile race along the coast of the Arabian Peninsula. It is thought their boat strayed into Iranian waters following mechanical problems.
Hashem Ahmadzadeh, an Iranian and Kurdish scholar at Britain's Exeter University, says it was clear the yachtsmen's entry into Iranian territorial waters had been a mistake - and so a political stand-off between Tehran and London was avoided.
"As Iranian political relations with the West is so fragile, one could expect that they could use this one. But fortunately this time they didn't - and probably they couldn't," he said.
Ahmadzadeh says relations between Britain and Iran have been tense since Iran's disputed elections earlier this year.
"Iran regularly has accused the British - especially the BBC Persian TV and Radio - as you know, mediums of interfering in Iran, Iranian's political internal affairs, and of course the Britains [sic] have always refused these accusations," he said.
This is not the first time Iranian authorities have captured British seamen. In March 2007, 15 British service personnel were taken hostage and held for 13 days.
Iran is right now holding three Americans who crossed the border into Iran from Iraq in July. The U.S. says the three were innocent hikers who crossed the border accidentally, but Tehran accuses them of spying.