Details are still to be finalized, but Muschamp will receive a raise boosting his salary to $900,000 starting in January. Muschamp, 37, arrived at Texas this season after previously serving as Auburn's defensive coordinator.
Brown, 57, said that he has no immediate timetable for leaving the job. He has eight years remaining on his current contract and hinted that he'd like to make another run at a national championship while still coaching.
"I won't be a Bobby Bowden or a Joe Paterno," Brown said. "But I'll be here a long time and as long as it works for me.
"For me, it's not any immediacy. I have eight years on my contract and plan on being here. It's exciting that Will would wait until the right time to move forward. Not many people would do that. I hope people don't think it's a twilight for me. It's a new beginning for all of us," he said.
Muschamp has already made a mark on a Texas defense that was expected to struggle because of its youth.
The Longhorns lead the Big 12 in rushing defense (82.5 yards per game) and scoring defense (19.5 points per game), good for 25th nationally in both categories. The Longhorns rank second nationally with four sacks per game, have limited all of their Big 12 opponents below their season scoring average and limited six of their opponents to 14 points or less.
"I was really excited when they presented the opportunity to me," Muschamp said. "I'm not in any hurry to be a head coach and hope Coach Brown's around for many more years. I'm just glad I'm going to be able to stay at Texas. This is the top program in the country, my family loves it here and there's no better person to watch and learn from about running a football program than Coach Brown.
"President [William Jr.] Powers, [men's athletic director] DeLoss Dodds, the administration and the leadership at Texas are outstanding. Coach Brown and a great support staff are in place. I've really enjoyed the kids in our program and everyone I've been around here. Texas has all the resources, facilities and a great recruiting base. It is the elite program in the country. No disrespect to any of the other places I've worked, but this is a really special place," he said.
Muschamp is a native of Rome, Ga., and a 1994 graduate of Georgia, where he was a four-year letterman at safety for the Bulldogs. He was selected as defensive co-captain as a senior and was a part of two bowl teams. He also earned a spot on the SEC Academic Honor Roll in 1993.
Will Muschamp, left, has been named the replacement for Mack Brown, who still has eight years left on his current contract.
The move is popular with Muschamp's family, who didn't want to move from Austin after living there for several months since arriving from his last job at Auburn.
"If I would have left, I would have left on my own because she was staying here," Muschamp said of his wife. "She really loves the community and the people, and our kids love their schools. It's just a special place and somewhere I want to be for a long time.
"I really appreciate the confidence that President Powers, DeLoss Dodds, the Board of Regents and Coach Brown have in me. I hope Coach Brown is here for a long time and look forward to continuing to coach our defense, learning from him and eventually carrying on the outstanding Texas tradition," he said.
After arriving at Texas in 1998, Brown has directed the Longhorns to a record of 113-26 in a career that has stretched 10-plus seasons. He's won or tied for four Big 12 South championships and also led Texas to three Big 12 championship game appearances, a Big 12 title and national title in the 2005 season.
Brown said he agreed to the move to ensure continuity in the Texas program.
"You want to see it continue working well," Brown said. "We've had some dips over the years and we don't want to have them again. We want to be a consistent winner forever. Texas fans deserve great football. My job and those for DeLoss Dodds and Bill Powers is to make it happen for a long time."
The announcement came after Muschamp had emerged as a top candidate for vacant jobs at schools like Clemson, Washington and Tennessee. Before he made a decision whether to interview, Texas officials decided to offer him a job-in-waiting for the future.
"He had to make a decision whether he wanted to go through interview processes or stay here," Brown said. "Open dates [like Texas has this week] is when they want you to come. All that is fair, but it becomes a big distraction. We decided yesterday to get it done today."
The announcement is also not expected to affect the staff, which is preparing for the Thanksgiving Day game with Texas A&M next week.
"Will is the hot guy and they understand that," Brown said. "This is not an immediate issue. It just means he's staying and not leaving. You all [the media] are more excited about it than anybody else. We're all going back to work. At some point way in the future it will become a factor."
Tim Griffin is a college football reporter for ESPN.com.