Members of Britain's Royal Yachting Association also said they were devastated by the news.
"Andrew is someone I've worked closely with since the age of 16 -- he was a great talent," performance director John Derbyshire said in a statement.
"He was a huge inspiration to others, both within the British Sailing Team and across the nation, and our deepest sympathies go out to his family at this terrible time."
Stephen Park, the Royal Yachting Association's Olympic manager, said Simpson was "a fantastic sailor who got the best out of everyone he sailed with. He was much loved and will be sorely missed by everyone in our close knit team."
The America's Cup is the oldest and most prestigious trophy in sailing, dating back more than 150 years. Teams from only four nations have won it: the United States, Australia, New Zealand and Switzerland. The New York Yacht Club held the cup for well over a century.
The Louis Vuitton Cup, the America's Cup Challenger Series, starts on July 7 and the America's Cup Finals begin on Sept. 7.
Artemis Racing represents the Royal Swedish Yacht Club, KSSS, Sweden's largest and oldest sailing club.