Chatwood, 27, will make $38 million over the course of the deal with the Cubs.
A six-year Major League Baseball veteran, Chatwood spent the past five years with the Colorado Rockies.
Chatwood has had stark home-road splits while calling hitter-friendly Coors Field his home.
For what it's worth, he also has an 0.69 ERA and 0.69 WHIP in two career starts at Wrigley Field. Pitching half his games at Coors Field, Chatwood actually has performed quite well but does come with some questions about how many innings he can pitch. On the road, he recorded a 3.49 ERA and held foes to a.200 batting average.
Since 2016, Chatwood is tied with Washington's Stephen Strasburg for the second-best road ERA in the NL at 2.57.
Chatwood's best season was 2013, when he had a 3.15 ERA in 20 starts. For his career, which included his first season with the Angels, Chatwood is 40-46 with a 4.31 ERA.
A second-round Draft pick by the Angels in 2008, Chatwood was traded to the Rockies in November 2011 for catcher Chris Iannetta. He figures to slot into the rotation behind Jon Lester, Kyle Hendricks and Jose Quintana.
The Cubs continue to be a leading suitor to land free-agent right-hander Alex Cobb, and they're one of seven finalists for Shohei Ohtani, the 23-year-old Japanses phenom who pitches and plays outfield.