In exchange, the Florida Panthers receive veteran Dan Ellis, who has a .908 save percentage, 2.75 goals-against average and 14 shutouts in 198 appearances with Dallas, Nashville, Tampa Bay, Anaheim and Carolina.
Thomas is 16-20-3 with Florida this season, with a 2.87 goals-against average and .909 save percentage.
Thomas, who turns 40 in April, signed with the Panthers as a free agent after taking a year off from hockey.
Dallas gets a goalie experienced in big games in the deal. Thomas has appeared in 50 post-season games, winning 29 with six shutouts, including Boston's Stanley Cup win in 2011.
Kari Lehtonen is the starter for the Stars, but froze in his lone playoff series, with Atlanta in 2007.
The trade means that Thomas and Roberto Luongo won't form a tandem. Luongo, who opposed Thomas in the 2011 Cup final with Vancouver, was traded the Panthers on Tuesday by the Canucks.
Thomas seemed taken aback by that deal when speaking to reporters after Florida's 4-1 loss to Boston on Tuesday night.
With Thomas and Ellis on the move, there's been a total of nine goaltenders traded since last week, following Ryan Miller, Jaroslav Halak, Viktor Fasth, Ilya Bryzgalov, Luongo, Jacob Markstrom and Devan Dubnyk.
Thomas didn't appear in the NHL until 2002-03, after several seasons in the minors and Europe.
The Flint, Mich., native rose to prominence with the Bruins despite his journeyman reputation, winning the Vezina Trophy as the NHL's top goalie in 2008-09 and 2010-11.
Thomas has amassed 31 shutouts, a .920 save percentage and 2.51 goals-against average in 418 career regular-season games.