Monroe signed his qualifying offer last offseason, when the Pistons decided not to offer him the max contract he was seeking. His idea was to play one more year in Detroit and enter unrestricted free agency after the 2014/15 season. There was risk involved but the gamble paid off for Monroe, who posted better numbers and thrived after Josh Smith was released mid-season.
While it was speculated he would not return to the Pistons, he never ruled out the possibility. Several teams were rumored to be interested in his services but at one point, him joining the Knicks was considered "a done deal." Monroe of course denied he had made up his mind, but with plenty of suitors, he was one of the hardest free agents to peg going into the offseason. When New York reportedly failed to offer him a maximum contract, his decision was made easier.
In his short five-year career, Monroe has showed he can be a solid post-scoring option, as well as provide acceptable rebounding from the center position. The questions marks come on the defensive end, where Monroe is neither mobile enough to guard in the perimeter nor explosive enough to be an elite rim protector. Playing out of position next to Drummond has made those problems more noticeable that they'd be if he was playing center, and he's young enough at 24 years old to still improve his awareness, but those are serious and real concerns.
With Monroe, it's all a matter of hiding his weaknesses and the Bucks are better equipped than most teams to do that. They were a fantastic defensive team last season and have a lot of long-limbed athletes who can cover ground, which will allow Monroe to stay close to the basket on defense. On offense, the former Piston will be a big upgrade over Zaza Pachulia, giving Milwaukee a solid post threat. The Bucks were looking for an improvement on their interior offense and Monroe represents that, even with his flaws.