"It's been a wonderful experience working at West Virginia, but I am making a decision that's best for my family," Graham said in a prepared statement. "I have two young children who are an hour away from Tulsa, and it's been a great strain emotionally and expense-wise to be so far away from them.
"West Virginia and Coach Rodriguez run a first-class organization, and this past season has been a magical year for me, one I will always cherish. The people of West Virginia and the atmosphere with our staff, our players and our fans has been truly great. This is a tough decision, but I know it will be best for our family."
Graham, who is a native of Mesquite, Texas, and a 1986 graduate of East Central University in Ada, Okla., played against new Tulsa head coach Steve Kragthorpe in college. Graham will begin work at Tulsa next week.
"We appreciate Coach Graham's efforts in helping build the West Virginia football program and helping turn things around this season," said WVU head coach Rich Rodriguez in a statement released by the sports information office. "As a staff, we emphasize the importance of family, so I can certainly understand Todd's decision."
Rodriguez said he has no timetable in naming a replacement.