During his time in Palo Alto, Crook was part of a two-year record of 23-4, as Stanford appeared in two BCS bowl games, won the Pac-12 championship in 2012 and, most recently, defeated Wisconsin 20-14 in the Rose Bowl on New Year's Day.
"He has helped developed winners at his stops and comes highly recommended. He brings a professional and positive attitude and expects toughness from the players. He has a proven track record as a teacher, coach and recruiter. He is a West Virginia native, who wants to be here, and I look forward to his contribution to our coaching staff."
Crook replaces Bedenbaugh, who was officially hired as the offensive line coach at Oklahoma on Feb. 17.
The new offensive line coach will have to help the Mountaineers reload at the position, as three veteran starters on the interior of the line -- left guard Josh Jenkins, center Joey Madsen and right guard Jeff Braun -- all exhausted their eligibility in 2012.
"One of the main reasons I wanted to come here was because I know how important football is in the state of West Virginia, especially the Mountaineer football program," Crook said in a prepared statement. "I'm very excited about this opportunity to work at a program with the history and tradition that it has. I understand the responsibility that it involves, and I don't take that lightly.
"I'm excited to be part of Coach Holgorsen's offensive system. When you're an offensive coach, you like scoring points. It was good to meet with [Holgorsen] and see his vision for the program. I look forward to working and learning from him and the other members of the staff. I'm excited to get started."
Before his time at Stanford, Crook spent eight seasons as offensive line coach at Harvard. He also was on the staff at Illinois in 2002, and previously was an assistant at several Division II schools in West Virginia, including West Liberty State, West Virginia Tech and Glenville State.