Perron, who had been an unrestricted free agent since July 1, will be playing in his 20th NHL season.
"We are excited to welcome David and his family to the Stars organization," Stars general manager Jim Nill said. "He brings a competitive mindset and a proven ability to perform in big moments. We believe his veteran leadership and skill set will be a valuable addition to our group as we continue to build toward our goal of winning a Stanley Cup."
Selected by the St. Louis Blues in the first round (No. 26) of the 2007 NHL Draft, Perron has 812 points (332 goals, 480 assists) in 1,239 regular-season games for the Blues, Edmonton Oilers, Pittsburgh Penguins, Anaheim Ducks, Vegas Golden Knights, Red Wings and Senators, and 64 points (26 goals, 38 assists) in 110 Stanley Cup playoff games.
Perron won the Stanley Cup with the Blues in 2019.
The Stars (3-3-1), who will be without forward Matt Duchene for three months because of core muscle surgery, visit the Chicago Blackhawks on Saturday (7 p.m. ET; Prime Video, CHSN).