Financial terms were not disclosed, but a source told ESPN's Jesse Rogers the contract is worth $38 million.
"Uber-talented right-hander moving into his prime," Cubs president of baseball operations Theo Epstein said of Chatwood. "He has great makeup. We think his best days are ahead of him. We're getting him into an environment where we think he can gain consistency with all of his pitches and play to his strengths a little bit more."
Chatwood, 27, was 8-15 with a 4.69 ERA in 33 appearances (25 starts) for the Colorado Rockies last season. His 15 losses tied for the National League lead.
Chatwood said he won't miss having Coors Field as his home ballpark.
"Yeah, it's going to be nice," Chatwood said. "Kind of be able to have the same routine and work on stuff and have your ball do the same thing, home and away, it's going to be pretty nice.
"I can focus on making my pitches. I can work on it more consistently, I would say. I don't have to worry about if it's going to move or if it's not going to move, or if I'm going to have to spin it different. Just focus on being more consistent and using my full arsenal instead of not using everything."
"There are times to strike quickly and there are times to lay back and get value," Epstein said. "Starting pitching was an area where we thought there was more demand than supply."
Chatwood missed the 2015 season following Tommy John surgery and returned in 2016 with his best season, also with the Rockies, when he finished 12-9 with a 3.87 ERA in 27 starts.
He is 40-46 with a 4.31 ERA in six major league seasons. He also has two saves in his career, including one last season.
"I feel really good," Chatwood said. "I felt strong all last year, you know, my velocity was up, and I think that was just the case of being healthy and being able to maintain it for two years and build off that."
"You have hopes, desires on what team you want it to be," Chatwood said of joining the Cubs, "and I was fortunate enough they were interested and obviously my family, talked to my agency, and it felt like a perfect fit."
Information from ESPN's Jesse Rogers was used in this report.