Gilbert, a junior, won a quarterback competition that also included Case McCoy, brother of former standout Longhorns quarterback Colt McCoy.
"The quarterback battle has been the best one that I've ever seen," Brown said. "I think that [first-year co-offensive coordinator] Bryan Harsin has done a tremendous job of making sure that each have had their opportunities with the different levels of competition."
Brown said he thought Gilbert's experience and on-the-field leadership helped him win the job "as much as anything."
Gilbert started all 12 games at quarterback for the Longhorns last season, completing 260-of-441 passes for 2,744 yards and 10 touchdowns, with 17 interceptions.
He gained some notoriety during his freshman season, when he replaced an injured Colt McCoy five plays into the BCS Championship Game against Alabama. He threw four interceptions during the game, but helped the Longhorns get back in the game during the second half before they eventually lost, 37-21.