A statement read on state media said the group was released into international waters after apologising. It comes at a sensitive time, as the US and Iran try to implement the deal on Iran's nuclear activities. A US official confirmed the sailors' release to the Reuters news agency. The incursion was "unintentional", a statement from the Revolutionary Guards quoted by state media said.
The Guards published pictures of the nine men and one woman being held
Earlier, the naval commander of the Guards, General Ali Fadavi, said investigations found a navigational failure was to blame. "We have concluded that passage of Americans in our territorial waters was not a hostile passage or for espionage or similar acts," he told Iranian television.
Iran-US relations pass a test: Jonathan Marcus, BBC diplomatic correspondent
The tentative and still largely potential softening of relations between Washington and Tehran in the wake of the nuclear deal seems to have passed a delicate initial test. The Tehran authorities have quickly accepted that the US patrol boats strayed into their waters by accident and the crews - according to Iranian State Television - have now been released. The process to begin lifting the sanctions imposed on Iran due to its nuclear activities is expected to get under way at the end of this week.
MORE