The person spoke on condition of anonymity Friday because Rhule had not yet formally accepted the position. Rhule was one of the final two candidates for the job.
Rhule was an assistant at Temple before joining the Giants as assistant offensive line coach in March.
Rhule played at Penn State and has 14 seasons of college coaching experience, with his last six at Temple. He was the Owls' co-offensive coordinator and tight ends coach in 2011. He also served as recruiting coordinator, helping Temple land the No. 1 class in the Mid-American Conference for 2011.
University of Miami defensive coordinator Mark D'Onofrio withdrew from consideration, the AP reported.
The Owls are in the market for a coach for the third time in the past three years, following Steve Addazio's departure to Boston College last week. Temple went 4-7 this season after having three straight winning seasons under Addazio and Al Golden.
Information from The Associated Press was used in this report.