Wright, a reliever who turns 29 on Jan. 28, was 0-4 with a 3.69 ERA in 70 games last season for Houston and Tampa Bay, which bought his contract in August. Wright had been the longest-tenured player on the Astros.
Wright, 10-15 with a 4.37 ERA in six big league seasons, became a free agent when Tampa Bay failed to offer a contract by the Dec. 2 deadline. In addition to his salary with the Cubs, he would earn a $25,000 bonus under Monday's deal for pitching 50 games or more.
Wright was selected by the Los Angeles Dodgers in the seventh round of the 2003 amateur draft and was taken by Houston in the 2007 winter meeting draft.