Tavares, who turns 23 this month, is the 14th captain in the team's 42-year history. He succeeds defenceman Mark Streit, who left as a free agent to join the Philadelphia Flyers.
"I'm honoured," Tavares said in a statement Monday. "To represent my teammates, coaches, management and the incredible fans that support this historic franchise is something that I take seriously."
Streit became the first Swiss-born team captain in NHL history when the Islanders appointed him in September 2011.
Tavares has led the Islanders in scoring in each of his first four NHL seasons. He had 28 goals — third most in the league — and 47 points while playing in all 48 games last season.
During the 2011-12 season, Tavares became an Islanders alternate captain. He is under contract through the 2017-18 season after agreeing to a six-year, $33 million extension in September 2011.
"My experiences over the past four seasons have prepared me for this responsibility, and I look forward to the challenge of leading the Islanders each season as we contend for the Stanley Cup," he said.
Tavares was a finalist for the Hart Trophy, given to the NHL MVP. In his playoff debut, he had a team-high five points, including three goals, in New York's six-game loss to Pittsburgh.
Tavares was the No. 1 overall pick in the 2009 NHL draft. He has represented Canada at four of the last five world championships.
"John has developed into an elite player in this league and become the leader of our franchise both on and off the ice," Islanders general manager Garth Snow said. "He consistently represents our organization with class and respect.
"John's work ethic and determination inspires his teammates to succeed, which makes him the perfect choice to lead our franchise."