Tavares had been the NHL's scouting system's top-ranked player all year, having produced 58 goals and 104 points last season for the London Knights in the Ontario Hockey League. He was that league's MVP and was also selected as the top forward at the 2009 World Junior Championships.
"John has been a game-breaking type of player at every level and will add a scoring touch to our lineup," Islanders General Manager Garth Snow said.
The NHL draft was also spiced by a trade that sent Anaheim defenseman Chris Pronger to the Philadelphia Flyers. Philadelphia sent rookie defenseman Luca Sbisa, forward Joffrey Lupul and two first-round picks -- one this year and another next year -- to the Ducks.
Pronger is entering his contract's final year, during which he will receive $6.25 million.
Defenseman Victor Hedman of Sweden was the second player chosen in the draft, going to Tampa Bay. Colorado selected Canadian center Matt Duchene with the third pick.
There were 10 Canadians and two Swedes chosen among the first 12 picks. The first American selected was defenseman Nick Leddy from Eden Prairie, Minn. He went with the 16th choice to the Minnesota Wild.