He has now released photographs of the happy couple, telling his five million Twitter followers he had been pleased to host the "delightful" pair after his team "helped stop [the] boat from wrecking".
Sir Ben and Ms Thompson, a sports broadcaster, were married in mid-December before flying to Antigua for their honeymoon. At the time, they issued a statement to say they "enjoyed a wonderful wedding at Hampton Court Palace" and "the honeymoon may involve a boat!".
Weeks later, Sir Ben, who has been crowned Olympic champion four times, America's Cup champion 11 times, world champion once and European champion nine times, experienced mechanical difficulties on his yacht, Rita, while sailing in the Caribbean.
Writing on his blog, Sir Richard said of Sir Ben: "Obviously he knows exactly what he is doing" at sea. "However, his boat had a serious mechanical problem, in no way Ben's fault, and he put a message out asking for help.
"Three of our wonderful watersports team (all of whom appeared in the Necker documentary last week) heard the call and raced over to their aid.
"The furling system broke on the main sail and the sail became so twisted that it couldn't go up, down, in or out.
"The only way to avoid going on to the reefs was for Marco to go to the top to cut the sail to pieces, whilst George and Ben were winching Marco up and down and Georgie was helping in the boat.
"Unsurprisingly, Ben kept an amazingly cool head whilst directing operations - he just needed more hands to sort out the mess."
Posting photographs of himself spraying champagne on the couple on the beach of Necker Island, Sir Richard added: "Many congratulations to Ben and Georgie on their marriage and we wish you both a lifetime of happiness, on land and sea!"
Ms Thompson has now sent a public message to thank him, saying: "Worse things have happened on honeymoon."