Weis is leaving the Chiefs after one year as offensive coordinator to accept an identical assignment with the Florida Gators.
McCoy joined the Broncos in 2009 when Josh McDaniels was hired as head coach. McDaniels handled play-calling but McCoy assumed those duties when McDaniels was fired on Dec. 6. The playbook and terminology that was employed by McDaniels and McCoy is comparable to what the Chiefs have utilized since Todd Haley became coach in 2009.
McCoy was under contract with the Broncos through the 2010 season, sources said.
Prior to joining the Broncos, the 38-year-old McCoy was hired in 2000 by the Carolina Panthers and served in a variety of offensive assistant posts, including quarterbacks coach and passing coordinator.
Kansas City was eliminated from the AFC playoffs after a 30-7 to the Baltimore Ravens on Sunday in the wild-card round.
Chris Mortensen is ESPN's senior NFL analyst.