They are said to have drifted into Iranian waters mistakenly while sailing from Bahrain to Dubai for a race.
Iranian radio said they had been freed at 0730 local time (0400 GMT). It is thought they were held on Siri island.
A statement by the Revolutionary Guard said interrogations had revealed their "illegal entry" had been "a mistake".
Luke Porter, 21, from Weston-super-Mare, Somerset, Oliver Smith, 31, from Southampton, Oliver Young, 21, from Saltash, Cornwall, Sam Usher, 26, from Scarborough, North Yorkshire, and Bahrain-based David Bloomer, who is believed to be in his 60s, were held on 25 November.
'Very relieved'
Iran's official IRNA news agency said the five had been freed after an interrogation by authorities established that their yacht had entered Iranian waters "by mistake".
A statement by Iran's Revolutionary Guard said: "After carrying out an investigation and interrogation of the five British sailors, it became clear that their illegal entry was a mistake.
"After obtaining necessary guarantees, it was decided to release them."
BBC correspondent Christian Fraser, in Bahrain, said he had spoken to Vanessa Bloomer, Mr Bloomer's wife, who said she had received no independent verification of the men's release.
Our correspondent added there was still a lot of uncertainty about what was happening.
The family of Mr Young also told the BBC that they had not heard anything officially but were keeping their fingers crossed and would go ahead with the previously-arranged plans to meet with Foreign Office officials in London.
David Young, Oliver's father, said he was "very relieved, obviously".
He added: "We thought this would be over quickly, and this is what we were hoping for."
Charles Porter, Luke's father, said: "We are not making any statement until we have proper confirmation from the Foreign Office.
"We are waiting for that confirmation."
Simon Drayton, brother of Sam Usher's fiancee, Nicola Drayton, added: "We are frantically trying to find out if it is true or not. We hope to God it is."
Andrew Pindar from Team Pindar, which was due to race the yacht the men were taken in, told the BBC that he was hopeful the reports were accurate.
He said: "I've had a call from Dubai this morning which suggests that the Iranian news release probably is true.
"I don't want to get carried away because until we see them safely in international waters it would be premature to count our blessings, but it does sound like they're on their way to safety."
'Lightning-fast'
The news comes hours after UK Foreign Secretary David Miliband spoke by phone to his Iranian counterpart.
The five were detained after the Revolutionary Guard stopped their Volvo 60 yacht, called The Kingdom of Bahrain, in the Gulf on 25 November.
Their families had been due to meet with Foreign Office officials later on Wednesday.
The BBC's Tehran correspondent Jon Leyne said the investigation had been "lightning-fast" by Iranian standards.
The Team Pindar-backed yacht was sailing from Bahrain to Dubai to take part in the Dubai-Muscat Offshore Race.
The 360-nautical mile Dubai-Muscat Offshore Sailing Race began on 26 November and ended two days later in the Omani capital's Bandar Al-Rawdah marina.
Race organisers said the five could have been "drifting" as a result of propeller problems.
The Kingdom of Bahrain yacht is owned by the Sail Bahrain project, which aims to promote the island as a yachting destination and was recently launched by Team Pindar.
Team Pindar is owned by G A Pindar & Son Ltd, a family owned print and publishing business based in Scarborough.
It is not the first time British sailors have been detained after being accused of straying into Iranian waters.
In March 2007 there was a prolonged stand-off between the UK and Iran after a 15-strong Royal Navy crew was detained by Iran's Revolutionary Guard.
And in 2004, eight British servicemen were held in Iran after being seized in the Shatt al-Arab waterway, where they were training the Iraqi river patrol service.
