Pavelski spent all of his previous 13 seasons with the San Jose Sharks, including the last four as captain.
The veteran forward, who turns 35 on July 11, racked up 38 goals in 75 regular-season games with the Sharks this past season, albeit with a career-high 20.2 shooting percentage. He added four goals and nine points in 13 playoff contests.
Pavelski ranks second on San Jose's all-time goals list with 355 tallies, trailing only Patrick Marleau. He also ranks third behind Marleau and Joe Thornton on the team's all-time points list (761) and all-time assists list (406).
Marleau, Thornton, and Marc-Edouard Vlasic are the only players to have played more games in a Sharks uniform than Pavelski, who skated in 963 regular-season contests for San Jose.
The Stars have been busy thus far in free agency. In addition to Pavelski, they signed Corey Perry and reportedly agreed to a deal with Andrej Sekera. The club is left with $2.47 million in cap space, according to CapFriendly.