Bedard, 33, began last season as the Pirates' Opening Day starter and ultimately posted a 7-14 mark with a 5.01 ERA in 24 starts before being released on Aug. 28.
He went 15-11 with a 3.76 ERA over 196 1/3 innings in 33 starts for the Baltimore Orioles in 2006 and set the franchise single-season strikeout per nine innings record (10.93) the following season.
Bedard won 28 games over a two-season span (2006-07).
The former Orioles ace has battled shoulder injuries since being dealt to the Seattle Mariners in 2008.
Bedard finished the 2011 campaign with the Boston Red Sox after being traded by Seattle as part of a three-team trade on July 31, 2011.
He inked a one-year, $4.5 million contract with the Pirates on Dec. 7, 2011.
The decision to bring Bedard into a rebuilding situation is a low risk, potential high-reward move by Astros general manager Jeff Luhnow.