Brown, who coached at Texas for 16 seasons and resigned in December 2013, will be part of coverage during the week and on ABC's College Football Countdown on Saturdays.
Davis, who coached at North Carolina from 2007-10 and Miami from 1995-2000, will work on ESPN2's day-long studio coverage every Saturday.
Brown told USA Today's Paul Myerberg he had discussed joining ESPN once he finished coaching for several years.
"We've kind of been talking about it over the three years," Brown said. "It wasn't a regular conversation, but it's something [ESPN President John Skipper] said: If and when you quit, we'd love to talk to you. He made that call, and I'm really excited about it."
Texas went 158-48 during Brown's tenure and won the 2005 BCS National Championship.
- Paul Palladino