Couture, who is entering his 11th season with the Sharks, was first drafted by San Jose in the 2007 NHL Draft.
Brent Burns, Tomas Hertl, Erik Karlsson and Joe Thornton will all serve as alternate captains this season.
Pavelski served as Sharks captain from 2014 up until the end of last season before signing a three-year deal with the Dallas Stars as a free agent.
San Jose head coach Peter DeBoer said Couture is a player who leads by example off the ice.
“He knows what it takes to win and his performance in our recent playoff runs reflects that,” DeBoer said Thursday in a statement. “Most importantly, Logan has the respect of his teammates and we’re extremely proud to name him as the tenth captain of the San Jose Sharks.”
Couture, 30, had a career best 70 points last season and led all skaters with 14 goals during the Stanley Cup Playoffs where the Sharks fell to the eventual champion St. Louis Blues in the Western Conference Final.
Couture has played in 663 games over his career with the Sharks and accumulated 507 points in the process.