Temple is expected to announce the hire Friday. Philly.com was first to report the news of Carey's hiring.
Carey, 47, compiled a 52-30 record and won two MAC titles during his tenure at Northern Illinois. The Huskies appeared in the conference championship in four of his six seasons.
Temple, which went 8-5 last season, has had a tumultuous time filling the position since Geoff Collins resigned Dec. 7 after two seasons to become Georgia Tech's head coach.
The Owls hired Miami defensive coordinator Manny Diaz to replace Collins on Dec. 12, only for Diaz to resign 17 days later to become the Hurricanes' head coach.
Diaz replaced Mark Richt, who abruptly retired Dec. 30.