Feldman's deal is for $6 million with the chance to earn an additional $1 million in incentives, a major league source told ESPNChicago.com's Bruce Levine.
Feldman, 29, has spent parts of the past eight seasons with the Texas Rangers and went 6-11 with a 5.09 ERA in 21 starts last season.
Cubs general manager Jed Hoyer said Feldman was signed to be a starter.
"I know he has bounced around a little bit with the Rangers, but in large part that was due to the amount of starting pitchers they had," Hoyer said. "We clearly see him as a starter, and we are excited to add him to the rotation."
After moving in and out of the rotation with the Rangers, Feldman is happy to get a starting shot with the Cubs.
"Starting is something I have always wanted to do during my career," Feldman said. "When (Cubs executives ) gave me the go ahead on that and let me know I was in their plans from the get-go it was something that made me very interested in coming (to the Cubs )."
Feldman's best season came in 2009, when he went 17-8 with a 4.08 ERA in 31 starts.
"That was a year where everything just started clicking for me," Feldman said. "For the first time in my career I was getting regular work in the starting rotation, and I got into a groove and got a lot of confidence getting out there every five days. Judging that season (2009 ) compared to this season I just feel like I am a better pitcher now even though the results were kind of a mixed bag for me last year. Confidence-wise and all my pitches, I believe I am able to do more now than I did in 2009."
Feldman, who was the Rangers' Opening Day starter in 2010, missed the first half of the 2011 season recovering from right knee surgery.
Cubs president of baseball operations Theo Epstein said he expects Baker, who missed all of 2012 after undergoing Tommy John surgery, to be ready for the starting rotation.
Garza, whose season was cut short with a stress reaction in his right arm, was recently cleared to resume his normal offseason routine. Garza had a scan of the area near his right elbow earlier this month and the results checked out normal with team orthopedist Stephen Gryzlo.
ESPNChicago.com's Bruce Levine contributed to this report.