It was no secret the Chicago Cubs would need to add rotation help this offseason.
Chatwood, 27, will make $38 million over the course of the deal with the Cubs.
Meanwhile, Chatwood led the league with 15 losses last season, going 8-15 with one save and a 4.69 ERA in 33 appearances with the Rockies.
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Chatwood has had stark home-road splits while calling hitter-friendly Coors Field his home.
Tyler Chatwood is getting a fresh start in the Windy City.
Part of the Cubs' belief is that Chatwood will find more consistency away from Coors Field. By comparison, Chatwood owned a 5-7 mark with a 3.49 ERA in 16 games on the road. He registered a 6.01 ERA and allowed foes to hit.302 at Coors Field last season.
Chatwood missed all of 2015 because of Tommy John surgery but is tied with Stephen Strasburg of the Nationals for second in the National League in road ERA the last two seasons (2.57). For his career, which included his first season with the Angels, Chatwood is 40-46 with a 4.31 ERA. He figures to slot into the rotation behind Jon Lester, Kyle Hendricks and Jose Quintana. Chicago also is waiting to see if Japanese two-way player Shohei Ohtani picks the Cubs, who are one of the seven finalists.