HMS Dragon diverted 500 miles to reach the 13 Britons and one American after the mast and rudder had broken off their 60ft (18m) yacht on Thursday.
The Clyde Challenger had been en route to the UK from the Azores after a four-month trip when it was damaged.
The navy's Type 45 Destroyer rescued the crew at 14:30 GMT on Saturday.
The Clyde Challenger was 610 miles south-west of Land's End when HMS Dragon arrived on Saturday.
'Desperate state'
