Anderson and Fuente fill the role previously occupied by Mike Schultz, who departed last month for the offensive coordinator position at Illinois.
Anderson will also switch from wide receivers coach to running backs. Fuente will move from running backs to quarterbacks.
Anderson will be in his 12th season at TCU. He was a graduate assistant his first three years before becoming the wide receivers coach in 2001 when Gary Patterson was named head coach.
Fuente enters his third season at TCU. He was previously at Illinois State for six years (2001-06), including the final three as offensive coordinator and quarterbacks coach. He began his collegiate playing career as a quarterback at Oklahoma before transferring to Murray State.
Burns most recently spent four seasons (2004-07) as the offensive coordinator at SMU. The Mustangs set a school record with 29 touchdown passes in 2006, while their 325 points scored ranked third all-time in SMU history.
At Cincinnati, Burns directed a record-setting offensive attack in 2002 that helped lead the Bearcats to the Conference USA championship. Cincinnati set school marks for passing yards (3,649 yards), total offense (5,565 yards) and points (409). The Bearcats led C-USA in passing (260.6) and total offense (397.5) per game.
It was Burns' second stint at Cincinnati. He was the Bearcats' quarterbacks coach from 1989-91. Burns also served three seasons (1992-94) as an assistant coach at Georgia Tech.
In his final year at Wyoming, Burns had the most improved offense in the Mountain West Conference.
Burns is a 1978 graduate of Springfield College, where he played quarterback. He also has a master's degree from Springfield. His first coaching position came at his alma mater as he served two seasons as offensive coordinator upon his graduation.
Burns and his wife, Debra, have two daughters: Kelly and Kirsten.