Fuente, 35, joined TCU in 2007 as the Horned Frogs' running backs coach. In 2009, he was promoted to co-offensive coordinator.
In his first two seasons at the helm of the TCU offense, the Horned Frogs set school records for touchdowns, points scored and first downs. From 2009-2010, the Horned Frogs won 25 of 26 games, including the 2011 Rose Bowl.
No. 15-ranked TCU went 10-2 this season and became the first team to win the Mountain West conference championship three years in a row. The Horned Frogs averaged 443.9 yards per game.
Fuente is arguably most notable for taking now Cincinnati Bengals rookie quarterback Andy Dalton under his wing. During his time at TCU, Dalton set school records in almost every major passing category.
In his interview with Memphis on Wednesday in New York City, Fuente, according to a source, "lit up the room" with his charisma and energy.
Alabama offensive coordinator Jim McElwain had been in line to accept the job before negotiations broke down, according to a source.
Fuente will be introduced tomorrow at noon at the Penny Hardaway Hall of Fame building.
Fuente began his college football career at Oklahoma and set a freshman-record for 11 touchdown passes. He transferred to Murray State after two seasons with the Sooners and set 11 offensive records with the Racers.