Baker, 31, has been on the disabled list all season recovering from Tommy John surgery. Signed to a one-year, $5.5 million contract in the offseason, Baker has rehabbed in the minor leagues, going 1-3 with a 5.46 ERA in eight starts for Class A Kane County and Daytona.
"He has done everything we have asked and he has worked his butt off," Cubs manager Dale Sveum said. "He has not had any setbacks and he deserves a chance to start."
Baker, who won 15 games for the Minnesota Twins in 2009, posted a 2.86 ERA through the first three months of the 2011 season before going on the disabled list with an elbow strain. He attempted a return late in the season, finishing the year with an 8-6 record and a 3.14 ERA. His last appearance in the major leagues came on Sept. 24, 2011 in Cleveland.
Baker, who pitched in one Cactus League game this spring for the Cubs before being shut down with soreness in the arm, said he lobbied for the chance to pitch against Milwaukee on Sunday.
"I don't think they would run me out there if they did not think I would do well," Baker said. "I do think that (a reward for his hard work) was definitely part of it. I appreciate that. It has been a long season for me and things have not worked out the way I wanted them to. You just try to end on a positive note."
Baker, who is 63-48 with a 4.15 ERA in his seven-year career, all with the Twins, said last week that pitching out of the bullpen would be something new and possibly unproductive for both sides at this point of the season.
"The last three or four rehab outings I really felt good," Baker said. "It was a matter of getting the innings and building up my endurance. Physically I feel great. I think surgery was a long time coming for me. I dealt with some elbow issues for a couple of years. It had become a real battle to stay loose and every start had become a process to even get out there."
Baker topped out between 85-86 mph in his rehab starts and his decreased velocity will be a challenge for a pitcher who maxed out at 92-93 mph during his best days pitching for the Twins.
"It just depends how much you value velocity," Baker said. "For me on the pitching hierarchy, it is movement, location and then velocity. I will definitely have to pay attention to the first two of those. (Without good velocity) you just don't get away with much. It is about making pitches. I am capable of making pitches down in the zone."
Baker has not been promised another start after Sunday or been told what his role would be the rest of the season.
ESPNChicago.com's Bruce Levine and Jesse Rogers contributed to this report.