The move comes only two days after former Mountaineers coach Dana Holgorsen was officially hired at Houston.
Brown, 38, is one of only six FBS coaches with 10 victories in each of the past three seasons.
Brown’s hiring was first reported by Yahoo! Sports.
A disciple of Hal Mumme’s and Mike Leach’s “Air Raid” offenses, Brown has a 35-16 record in four seasons at Troy. After going 4-8 in his first season, the Trojans are 31-8 the past three seasons combined and won three bowl games. They won the 2017 Sun Belt Conference title and were co-Sun Belt East champions this past season.
In 2017, the Trojans upset No. 25 LSU 24-21, which ended the Tigers’ 49-game nonconference winning streak at Tiger Stadium.
Holgorsen went 61-41 in eight seasons at West Virginia.
ESPN’s Jake Trotter contributed to this report.