Broxton was traded to the Cincinnati Reds just before the deadline Tuesday for two minor league pitching prospects, left-handed reliever Donnie Joseph, 24, and right-handed starter J.C. Sulbaran, 22.
Broxton, a two-time National League All-Star with the Dodgers, logged 23 saves in 27 opportunities for Kansas City. He had elbow surgery last September and signed with the Royals in November to be a setup man for Joakim Soria.
That changed when Soria had season-ending elbow surgery in spring training.
"I wasn't supposed to close, but Soria got hurt," Broxton said. "I stepped in and threw the ball fine. My arm felt fine.
"They've got a bunch of talent in here. They're not far away from winning here either. I came here to be a leader to some of these young guys. I hate I've got to go, but I've got to go."
Broxton goes from a club in last place to a team leading its division.
"I'm going somewhere where I'm picking up 20 to 25 games," Broxton said. "I enjoyed my time here, but this is part of baseball, so go over there and hopefully we can win a division over there."
Holland, who has four major league saves, takes over as the ninth-inning man.
"He's been very solid down there. We'll give him an opportunity to close games out," manager Ned Yost said. "He was pretty obvious for me right now. He's been pretty consistent, and we feel his stuff is all the way back to where it was last year, when he was really successful."
The Royals didn't have a save situation Tuesday in their 8-3 win over the Indians.