Brown, who has coached the Longhorns since 1998, has come under fire while his teams have produced a 21-16 record over the past three seasons.
That streak followed a stretch of nine straight double-digit win seasons that included seven straight bowl victories and a national championship.
"Now that the Longhorn football team has finished its regular season, there has been an increase in media speculation about Coach Mack Brown's future," school president Bill Powers said in a statement.
"I'd like to state unequivocally that Coach Brown has my full support as well as the support of Men's Athletics Director DeLoss Dodds. Put succinctly, Mack Brown is and will remain the Longhorns' head football coach.
"Coach Brown restored Texas' winning tradition. He embodies the Texas character, is a superb ambassador for the University of Texas, and runs a program that is both winning and clean, a program that all alumni and fans can and should be proud of."
Brown, 61, has an overall record of 149-43 with Texas and his teams have gone 91-31 in Big 12 Conference play.