He finished with a 4.69 ERA while moving in and out of the starting rotation, and his 77 walks were fourth-highest in the majors.
Chatwood, 27, will make $38 million over the course of the deal with the Cubs.
It was no secret the Chicago Cubs would need to add rotation help this offseason.
The former Rockies right-hander signed a three-year, free-agent contract with the Chicago Cubs Thursday.
Chatwood was 8-15 with a 4.69 ERA in 33 appearances (25 as a starter) with the Rockies last season, tying for the most losses in the NL.
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It had been hoped that construction would get under way by 2016, but so far the stadium is yet to be granted planning permission. Group A games will be played in Rome and Baku, while Group B games will take place in Saint Petersburg and Copenhagen.
Chatwood has had stark home-road splits while calling hitter-friendly Coors Field his home.
More runs were scored at Coors Field than any other park in 2017, per ESPN. Montgomery had a 4.15 ERA as a starter and a 2.49 ERA as a relief pitcher past year. On the road, he recorded a 3.49 ERA and held foes to a.200 batting average.
In 2016 Chatwood posted a 12-9 mark with a 3.87 ERA.
Chatwood, a second-round pick by the Angels in 2008, spent seven seasons with the Angels and Rockies, but missed the entire 2015 after undergoing reconstructive elbow surgery. For his career, which included his first season with the Angels, Chatwood is 40-46 with a 4.31 ERA.