In exchange, the Rockies sent minor league pitchers Wes Musick and Jonnathan Aristil to Houston in a deal that was announced Thursday.
The trade was first reported by ESPN The Magazine's Buster Olney.
Lindstrom, eligible for salary arbitration, has made at least 50 appearances in all four of his seasons in the majors. He had a team-high 23 saves for the Astros in 2010, finishing 2-5 with a 4.39 ERA.
"We were very reluctant to trade Matt," Astros general manager Ed Wade said. "But with Brandon Lyon, Wilton Lopez and some of our younger arms, we think we have good coverage at the back of the bullpen."
Given his experience as a closer, Lindstrom could be insurance for the Rockies in case anything happens to Huston Street, who missed the first 69 games in 2010 as he recovered from an inflamed right shoulder.
Lindstrom could also join Rafael Betancourt as a primary setup man.
A converted position player, Aristil, 24, spent time at three different levels in the Rockies' organization last season, winding up at Triple-A Colorado Springs where the right-hander threw two scoreless innings.
The left-handed Musick started 23 games at Class A Asheville, turning in an 8-7 record with a 4.05 ERA.
"We've added two young arms to our prospect depth and we think both Aristil and Musick have a chance to help us down the road," Wade said.
Information from The Associated Press was used in this report.