News of their release was confirmed by the Foreign Office and the Iranian Ministry of Foreign Affairs this morning, and the yachtsmen are now being towed to international waters.
Sail Bahrain's Kingdom of Bahrain Volvo 60 racing yacht was stopped by Iranian navy vessels on 25 November.
The crew were on their way from Bahrain to the Dubai-Muscat Offshore Sailing Race. It is thought their boat inadvertently strayed into Iranian waters.
Andrew Pindar, chairman of Sail Bahrain, told PrintWeek that news of their release was a relief. He said: "I'm very glad the families are to be reunited with their loved ones. Hopefully, that is the end of the story."
An earlier statement from Pindar on the Sail Bahrain website said: "We received confirmation from the Foreign Office at 8:30 this morning that our sailors had been released by the Iranian authorities. We are all absolutely thrilled with the news.
"It has been an extremely worrying time for all of us and particularly for the families and loved ones of those on board."
The team has sent out a boat to meet the crew, where team director Nick Crabtree will accompany them to shore.
Pindar added: "I would like to take this opportunity to thank the Foreign Office and the British and Bahrain Embassies for all their help and for bringing the matter to a swift conclusion – and to the Iranian authorities for their understanding."
UK foreign secretary David Miliband welcomed the sailors' release, claiming that it proved "diplomacy can work".
"I have had confirmation that they are now heading towards international waters on their way to Dubai. I welcome the fact that this has been dealt with in a professional and straightforward way by the Iranian authorities," he said.