Texas Men's Athletics Director Steve Patterson said Mack would step down after the Dec. 30 Alamo Bowl, ending weeks of speculation over his job security.
"We appreciate everything Mack has done for the University of Texas," Patterson said. "He's been a tremendous coach, mentor, leader and ambassador for our university and our student-athletes. He is truly a college football legend."
Brown will leave after 16 seasons guiding the Longhorns, including a national championship after the 2005 season.
"We built a strong football family, reached great heights and accomplished a lot, and for that, I thank everyone," Mack said. "It's been a wonderful ride."
However, he added, the program now is "being pulled in different directions, and I think the time is right for a change."
"I sincerely want it to get back to the top and that's why I am stepping down after the bowl game. I hope with some new energy, we can get this thing rolling again."
Brown had come under criticism after Texas finished with an 8-4 record this season, its fourth straight of at least four losses. The Longhorns have gone 30-20 since falling to Alabama in the 2010 BCS National Championship.
Jessica Simpson shares three-way kiss with friends in photo
Senate Democrats to pull all-nighter on climate change