The 35-year old Fuente has been with the Horned Frogs for five years, first serving as a running back coach before being promoted to quarterback coach and co-offensive coordinator in 2009.
"He will do well and work hard to make Memphis a better place," TCU head coach Gary Patterson told the Forth Worth Star-Telegram.
Fuente's hiring makes him one of the youngest active head coaches in FBS, behind only Western Kentucky's Willie Taggart, signifying his place as one of the rising stars in the profession.
Memphis, a member of Conference USA, has never had much success as a football program. In 52 years in the FBS, the Tigers have played in only six bowl games.
However, it is located in a fertile recruiting area, annually producing players like Michael Oher, the Baltimore Ravens OT whose life was famously chronicled in The Blind Side.
The Tigers previous coach, Larry Porter, went 3-21 in his two years in Memphis.
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