Gase, 34, was the quarterbacks coach for the Broncos for the past two seasons. He was the wide receivers coach for two seasons before that. He has been a coach or a scout in the NFL for eight seasons.
Gase replaces Mike McCoy, who left the team and became the head coach of the San Diego Chargers on Tuesday.
Gase is one of the youngest offensive coordinators in the NFL.
Ken Whisenhunt, the former head coach of the Arizona Cardinals, and former Cleveland Browns head coach Pat Shurmur were considered for the position, according to Klis.
Gase coached future Hall of Famer Peyton Manning this year in his first season as a Bronco. Manning, who missed all of the 2011 season with the Indianapolis Colts, rebounded well, completing 68 percent of his passes for 4,659 yards and 37 touchdowns. He threw just 11 interceptions.