The Broncos confirmed the move.
To acquire Cutler, the Bears had to give up quarterback Kyle Orton and first-round picks in 2009 and 2010, a source said.
To complete the trade, the Broncos had to give back an undisclosed draft choice in a later round.
The Bears beat out the Redskins, Buccaneers, Lions, Titans and other teams to get land the 25-year-old Pro Bowl quarterback.
The Broncos had been asking for at least two first-round choices.
Cutler asked to be traded when he found out first-year coach Josh McDaniels tried to acquire Matt Cassel in a trade with the Patriots.
Cutler had not returned phone calls from the Broncos, according to the team, and had been staying away from the offseason program.