Houston sent two low-level minor leaguers and a player to be named to the Marlins.
Lindstrom features a fastball that can reach 100 mph, though he sometimes has trouble harnessing all that power.
The 29-year-old righty went 2-1 with 15 saves in 17 chances and a 5.89 ERA in 54 games for Florida last season. He was hurt by four bruising appearances, in which he allowed 18 earned runs in only 2 1/3 innings.
Houston needed another reliever after closer Jose Valverde and setup man LaTroy Hawkins filed for free agency. Hawkins agreed to a contract with Milwaukee earlier in the day, subject to completion of final details.
"We're happy to have Matt as a part of our club," Astros manager Ed Wade said. "He has a tremendous arm and has shown closer's stuff in the past. He had some health issues last season, but we believe he'll bounce back. We feel he has the capability to be our closer or to at least share those responsibilities."
The cost-conscious Marlins had a major league-high 11 players eligible for salary arbitration, including Lindstrom.
Florida got right-hander Robert Bono and infielder Luis Bryan. The 20-year-old Bono was 10-8 at Class A Lexington and the 19-year-old Bryan hit .340 with two home runs and 19 RBIs in 31 games in the rookie Gulf Coast League.