The deal, announced Friday, includes a $50,000 performance bonus if the left-hander appears in 60 games.
The 29-year-old had a 3.17 ERA in 58 games with the Chicago Cubs in 2014, his third straight season with at least 55 appearances. He allowed two home runs in 48 1-3 innings.
Selected by the Dodgers in the seventh round of the 2003 amateur draft, Wright is 10-18 with a 4.17 ERA in 360 games with Houston, Tampa Bay and the Cubs. Chicago failed to offer a contract by the Dec. 2 deadline, allowing him to become a free agent.
Wright has limited left-handed hitters to a .238 average in 591 plate appearances.