"We appreciate all the hard work that Brandon did during his three years in Denver and wish him the best with the Rams," Elway tweeted.
The trade reunites Lloyd, who is in the final year of his contract, with former Denver head coach Josh McDaniels, the Rams' offensive coordinator, under whom he enjoyed his greatest success last season.
Lloyd led the league in 2010 with 1,448 yards on 77 receptions and scored 11 touchdowns.
This season, Lloyd has caught 19 passes for 283 yards and no touchdowns.
ESPN has reported that the Rams will give up a sixth-round pick, but it will become a fifth-rounder if Lloyd catches 30 more passes the rest of the season.