"We appreciate all the hard work that Brandon did during his three years in Denver and wish him the best with the Rams," John Elway, Denver's head of football operations, said in a message sent via Twitter.
Lloyd was the NFL's most prolific pass catcher last season, piling up 1,448 yards and 11 scores on 77 receptions. So far this season, he has 19 receptions for 283 yards and no touchdowns.
Lloyd, in the final year of his contract, will be working with Rams offensive coordinator Josh McDaniels, who was Denver's head coach last season.
ESPN reported the 0-5 Rams will give the 1-4 Broncos a sixth-round pick, but it will become a fifth-rounder if Lloyd catches 30 more passes this season.