The 36-year-old Briton was trapped underwater Thursday after his catamaran capsized while training in San Francisco Bay for the America's Cup.
Simpson was one of Britain's leading sailors, having won a gold medal at the 2008 Beijing Olympics and silver at last year's London Games.
"Andrew Simpson was a hugely accomplished sailor and Olympian," Rogge, a former Olympic sailor from Belgium, said in a statement to The Associated Press. "He died pursuing his sporting passion and our thoughts are naturally with his family and friends and of course his fellow crew members who must be devastated by this tragic accident."
The British Olympic Association described Simpson as a "treasured and accomplished member" of its teams.
"Andrews's talent and humour was an inspiration to others and he will be sorely missed by the Olympic family," the BOA said.
Officials have launched an investigation into the accident, which unfolded after Simpson's Artemis Racing boat flipped.
Stephen Barclay, CEO of the America's Cup Event Authority, said it was unclear what effect the death will have on the America' Cup races, which are scheduled to run from July to September.