The Cubs announced the agreement on Thursday.
Chatwood is joining a team with three straight NL Championship Series appearances and a World Series title in 2016. He figures to slot into the rotation behind Jon Lester, Kyle Hendricks and Jose Quintana.
Chatwood, who turns 28 next week, was 8-15 with a 4.69 ERA in 33 appearances, including 25 starts, for Colorado last year. He is 40-46 with a 4.31 ERA over six seasons with the Los Angeles Angels (2011) and Rockies (2012-14, 2016-17). He was limited to four starts in 2014 and missed the 2015 season because of Tommy John surgery.
