Nagy, fired last month after four seasons as head coach of the Chicago Bears, returned to the Chiefs on Friday as senior assistant and quarterbacks coach.
Nagy, 43, was with the Chiefs for five seasons from 2013 through 2017, finishing as offensive coordinator his final season, when Mahomes was a rookie and the backup quarterback to Alex Smith.
Nagy was co-offensive coordinator in 2016 and quarterbacks coach his first three seasons in Kansas City.
Nagy was 34-31 in the regular season for the Bears, including 6-11 last season. He was the NFL's Coach of the Year in 2018 for leading the Bears to a 12-4 record and the NFC North championship. He took the Bears to the playoffs twice but failed to win a game either time.
Nagy replaces Mike Kafka, who left the Chiefs to become the offensive coordinator for the New York Giants.