The White Sox, who are seven games behind the first-place Cleveland Indians in the AL Central, added Morneau and Fulmer as part of a series of roster moves before Friday's game against the Los Angeles Angels.
Morneau, a former American League MVP, signed a one-year, $1 million deal with the White Sox last month after undergoing offseason elbow surgery. He batted .174 in eight games during his minor league rehab assignment over the past 11 days.
Fulmer was the No. 8 pick in last year's draft and appeared in the All-Star Futures Game this past weekend in San Diego. The right-hander has pitched exclusively as a starter in the minors, but the White Sox reportedly are considering using him out of the bullpen.
"You're trying to see if a kid can do it, and we did it with Carlos a little bit, and Chris has done it," Ventura told the Chicago Tribune. "You bring 'em up here and you bring 'em through out of the bullpen and see if you can lighten their load a little bit and then see how they handle it."
Atlanta Braves top prospect Dansby Swanson, Fulmer's college teammate at Vanderbilt, tweeted Friday morning to congratulate Fulmer.
Morneau won the 2014 NL batting title when he hit .319 for Colorado. He was the MVP in 2006 with Minnesota when the Twins fought the White Sox for supremacy in the AL Central.
Morneau also batted .310 in only 49 games with the Rockies last season. He's had concussion issues and has been slow to recover from surgery to repair the primary flexor in his elbow.
Fulmer, 22, is 4-9 with a 4.76 ERA in 17 starts this season at Double-A Birmingham. But he has pitched better over his past three starts, allowing just two runs over 19 innings.
"I'm just getting ahead," Fulmer told MiLB.com over the weekend. "I felt like I fell behind a lot of guys and I paid for it. I'm just coming out with a strike-one mentality and just pounding the strike zone."
In a corresponding roster move Friday, the White Sox optioned outfielder Jason Coats to Triple-A Charlotte.
Information from The Associated Press was used in this report.