The forward, who turns 35 on July 11, had 64 points (38 goals, 26 assists) in 75 regular-season games with the San Jose Sharks last season and nine points (four goals, five assists) in 13 Stanley Cup Playoff games.
Selected by San Jose in the seventh round (No. 205) of the 2003 NHL Draft, Pavelski has 781 points (355 goals, 406 assists) in 963 games, all with the Sharks. He had 100 points (48 goals, 52 assists) in 134 playoff games and was named Sharks captain Oct. 5, 2015.
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He is second on the Sharks' in goals, behind Patrick Marleau (508), third in assists and points, and fourth in games.
Pavelski said he wasn't just looking to sign with the highest bidder.
"There were definitely some boxes that we wanted checked off," he said. "We wanted to feel that the team was close to winning. And playing against the Stars, playing against some of their players, and the season they had, they were a team that checked … a lot of the boxes.
"We came in and spent a couple of days there with some of the management, saw the city, the youth rinks, schools, neighborhoods, and just really tried to visualize ourselves being here and it seemed like a perfect fit for us."