Simpson — who won Olympic gold in Beijing and silver at London 2012 — was training for the America’s Cup when his 72-foot catamaran flipped over in San Francisco Bay on Thursday, trapping him underneath for 10 minutes.
He was taken to shore but doctors were unable to save him.
The 36-year-old was the strategist for the Swedish team Artemis ahead of this summer’s epic sailing race, Ainslie represents for rival crew Oracle.
Ainslie said: “Today is a sad day for all of us in the sailing community.
“Andrew Simpson was a great person, a terrific sailor, and a good friend to all of our team. He will be dearly missed.”
Spurs fan Simpson — nicknamed Bart — won gold in the Star class at Beijing 2008 with lifelong pal Iain Percy.
They first met as eight-year-olds at a Lego tournament.
John Derbyshire was the performance director for Britain’s Royal Yachting Association, coaching the pair as teenagers.
He said: “Bart was one of the top sailors. It’s a really big shock, totally unexpected.
“These are big powerful boats but you don’t associate them with fatalities. It’s very sad.”
America’s Cup chief executive Stephen Barclay insisted he would wait for the full details of the accident before deciding whether changes should be made to the race, which opens on July 4.
He said: “Boats follow these vessels with divers and doctors and the like on board in case these things happen and those procedures were followed.
“It’s a tragic day for us at the America’s Cup and for sailing in general.”
The Americas Cup is one of the oldest, most prestigious prizes in sport. Simpson had switched his focus to the event after the Star class was dropped from the 2016 Olympic Games in Rio.