Back from Tommy John surgery, the right-hander makes his Cubs debut Sunday against the visiting Milwaukee Brewers.
Baker went 63-48 with a 4.15 ERA in 163 games - 159 starts - for Minnesota from 2005-11, then underwent elbow surgery in April 2012. Chicago (60-81) signed him as free agent late last year.
After spending some time rehabbing at the team's facility in Arizona, Baker allowed 18 earned runs and 34 hits with 16 strikeouts and 10 walks over 29 2-3 innings between Class-A Kane County and Class-A Daytona.
His last major league appearance came with the Twins on Sept. 24, 2011, and most recent start Aug. 8 of the same season.
"It's been a long while since I started a major league game, and there's definitely a lot to be excited about," Baker told the Cubs' official website. "Regardless of the results, I think you go out there and do the best you can and enjoy it. You never know when things are going to be taken away from you. You appreciate every start."
Sveum said earlier in the week that Baker would not start the series finale, but the veteran successfully lobbied his case to his manager and pitching coach Chris Bosio.
"They definitely valued my opinion," said Baker, who is not expected to be on a limited pitch count. "I said, 'I feel like I need to pitch, I want to pitch.' I appreciate the opportunity to get back out there. It's going to be fun for sure."
He'll try to help the Cubs bounce back from Saturday's 5-3 loss to Milwaukee (61-80) and finish 5-4 on this homestand.
Chicago could face a serious challenge from Yovani Gallardo (10-9, 4.31 ERA), who is 2-0 with a 1.37 ERA in four starts since coming off the disabled list with a strained left hamstring.
"Very pleased," Gallardo told the Brewers' official website about his performance since returning from that injury.
The right-hander has lasted seven innings in two straight starts, most recently Tuesday when he gave up two runs during a 4-3 loss to Pittsburgh.
Gallardo, however, has not been able to complete five innings in two starts against the Cubs this season, going 0-1 with a 6.23 ERA.
Chicago first baseman Anthony Rizzo is 11 for 24 in his last seven home games against the Brewers, and 4 for 9 with a double versus Gallardo.
Luis Valbuena's two-run homer gave the Cubs an early 2-0 lead Saturday, but Logan Schafer delivered a three-run triple as the Brewers scored four times in the fourth and won for the second time in three games since losing five in a row.
Despite the big hit, Schafer is batting .224 overall, and is 4 for 25 against the Cubs in 2013.
"Well, Schafer is off and on," manager Ron Roenicke said. "I don't want to say much he's been struggling for us, but he has been getting some big hits for us."