The White Sox, who were playing at Kansas City, also acquired right-hander Doug Nickle, and sent right-hander Scott Dunn and left-hander Tim Bittner to the Angels in the deal.
Schoeneweis, the Angels' player representative and the only lefty in their bullpen, made 47 starts the previous two years -- but has been used exclusively in relief this season by Anaheim manager Mike Scioscia. He learned of the trade after the team did its stretching before their game against the Yankees.
"I never asked for a trade," said Schoeneweis, who is 1-1 with a 3.96 ERA in 39 relief appearances this season. "I did tell Mike, 'If you don't plan on using me, why am I here?' But the talks I've had with Mike haven't been bitter. As a manager, he expects the players to want to play and to voice that opinion. And I did that.
"Once the season started and I was in the bullpen, I couldn't control that. So I just went out and tried to pitch well, but I knew that pitching well in that role would keep me in that role. So there really wasn't much that could change it."
Schoeneweis was replaced in the rotation late last June by right-hander John Lackey. The Angels went on to win their first World Series title -- with Lackey winning the clinching seventh game. Schoeneweis was 3-2 with a 3.25 ERA and one save in 39 appearances out of the bullpen.
"I had two options," Schoeneweis said. "I could either be angry about it and make waves and try to get myself out of there, or do what I did."
Scioscia had nothing but praise for Schoeneweis on his final day with the team.
"Schoney was a big part of our second-half surge," Scioscia said. "A lot was said about John Lackey coming up when we rearranged the staff, and John certainly did a terrific job. But what can't go unnoticed is the job Schoney did in the pen."
Schoeneweis, 29, has a 28-31 career record with a 5.10 ERA in 183 games, including 74 starts.
"Right now, our primary need for him is in the bullpen," White Sox general manager Ken Williams said. "He's not stretched out enough to go into the rotation."
Williams said Schoeneweis will be given a chance in spring training to win a spot in the starting rotation.
"He has three quality pitches," Williams said. "We can visualize him in our rotation next year."
Nickle was 2-2 with four saves and a 1.48 ERA in 34 relief appearances with Triple-A Salt Lake City. He will be assigned to Triple-A Charlotte.
Glover, 26, was 1-0 with a 4.54 ERA in 24 relief appearances with Chicago.
Dunn, 25, was 3-1 with a 1.69 ERA in eight relief appearances with Double-A Birmingham after being acquired July 6 in a trade with Cincinnati for infielder D'Angelo Jimenez.
Bittner, 23, went 4-4 with a 3.40 ERA in 10 starts for Class A Kannapolis and 3-3 with a 3.60 ERA in 17 relief appearances for Class A Winston-Salem.