The contract is worth $10 million and contains a mutual option for 2014.
Capuano will be paid $3 million in 2012 and $6 million in 2013, a source told ESPNLosAngeles.com's Tony Jackson. At the end of the deal, Capuano would be paid a $1 million buyout or earn $8 million in 2014 under the mutual option.
The deal also includes performance bonuses that would pay Capuano $75,000 each for passing 160, 170, 180, 187 and 195 innings pitched, the source said.
Capuano would earn another $250,000 performance bonus if he pitches a combined 360 innings in 2012-2013, according to the source.
"Chris is an established major league starting pitcher who adds to our staff," Dodgers general manager Ned Colletti said.
Capuano spent 2011 with the New York Mets, going 11-12 with a 4.55 ERA in 31 starts in his return from Tommy John surgery. He struck out 168 batters and walked 53.
The seven-year veteran, who spent five of those seasons with the Milwaukee Brewers, has a 57-64 career record and a 4.39 career ERA in 181 appearances, 153 of them starts.
Capuano had career highs of 18 wins (18-12), 176 strikeouts and 35 starts with the Brewers in 2005 and was an All-Star in 2006.
Information from ESPN.com senior baseball writer Jayson Stark, ESPNLosAngeles.com baseball writer Tony Jackson and The Associated Press was used in this report.