Hopes of finding the four men, who were sailing across the Atlantic Ocean, faded on Friday after the capsized vessel was found with its life raft still on board.
The heartbreaking discovery led to the US Coast Guard calling off its search for experienced captain Andrew Bridge, 22, from Farnham, Surrey, and crew members Steve Warren, 52, from Bridgwater, Somerset, Paul Goslin, 56, from West Camel, Somerset, and James Male, 23, of Southampton.
The families issued a statement through the Foreign Office which said news "brought us unimaginable pain".
They added: "Nonetheless, we take some small solace that this conclusive development allowed us to gain an element of closure. We know that they will be forever remembered based upon the flood of touching responses received already.
"The UK Foreign Office has been relentless, professional and hugely sympathetic throughout and we thank them unreservedly. Naturally we'd like to thank the US Coast Guard, along with some UK and Canadian support.
"We are well aware that the men and women of the US Coast Guard who tirelessly participated in the search, plus those on private yachts and merchant vessels, bore terrible weather conditions and not inconsiderable personal risk to find our loved ones: we offer our eternal gratitude."