Chicago and Kansas City announced the trade late Monday. Maldonado, 32, is a career .220 hitter with 57 home runs. The nine-year veteran is joining his fifth team since 2016.
Montgomery, 30, provided the final out for the Cubs' 2016 World Series winning team. He has a 3.72 ERA and 56-41 record in 167 games. He was initially selected by the Royals as the No. 36 overall pick in the 2008 MLB June Amateur Draft.
"You threw the most important pitch in Cubs history and we will be forever grateful for what you helped bring the city of Chicago.Thank you to a true champion," the Cubs tweeted Monday.
The Cubs made the move after starting catcher Willson Contreras sustained a strained right foot. The Cubs placed Contreras on the 10-day injured list. He hasn't played since July 13.
Montgomery is expected to start for the Royals against the Cleveland Indians Friday in Cleveland.
"We started talking about this deal a couple days ago," Royals general manager Dayton Moore said, according to MLB.com. "[Montgomery] wants to start, and we can give him that opportunity.
"This was an opportunity to get him back to our organization. The money is pretty much a swap. But we'll have two years of club control [after this year]. It's just a good baseball deal."