The six had been at sea for 27 days when the 11.1m boat, Sara G, overturned at 520 miles from their destination yesterday.
The rowers were picked up from a raft, which they had lashed to the hull of their overturned vessel by a Panamanian cargo ship.
A coastguard spokesman added: “They are all safe and well on board and proceeding to Gibraltar, where they are due to arrive on 9 February.”
The Atlantic Odyssey website names the crew as captain Matt Craughwell; Ian Rowe, a 45-year-old father of four; Aodhan Kelly, 26, from Dublin, Ireland; Simon Brown, 37, a father of three from Wiltshire; father-of-two Yaacov Mutnikas; and 29-year-old Mark Beaumont (above), a documentary-maker from Perthshire.
The website states that they were rowing from Tarfaya in Morocco to Port St Charles in Barbados with the aim of becoming the first crew in history to break the sub-30-day barrier, calling it “ocean rowing’s very own four-minute mile”.
The Sara G is the second boat this winter to encounter trouble attempting to cross the Atlantic. In December, two transatlantic rowers, one of them British, were rescued from a life raft in the middle of the ocean after their small boat sank in rough seas.