Mr Moore, currently principal of Stratford-upon-Avon College, will take the top job at Stoke on May 1. He will be taking on one of the highest-profile rescue jobs in education, with Stoke facing an Pounds 8 million cash crisis after sacking its principal and deputy over allegations of bullying and running a pub while on sick leave.
A Coopers Lybrand report on the crisis and the Further Education Funding Council's inspection report on the college are due to be completed within weeks.
Mr Moore said: "I strongly support the necessary steps being taken by my new colleagues to place the college on a sound financial footing once again. "
Chairman of the Stoke corporation Kevin Farrell said the college had turned the corner and could look forward to long-term financial stability, high-quality courses and real growth.
He said: "Hopefully Graham's appointment will mark the end of our period of backward-looking. What's gone has gone and what's done is done. It is probably the cornerstone of all the elements in the recovery plan.
"He will provide the leadership and the commitment and the momentum in the longer term. It's the most challenging job in FE but it's the one for exactly the same reasons that will repay effort and commitment."
He said the college had turned the corner. "The mood is better in the college and we are winning the commitment of all the staff. We are operating a briefing system and have held consultations with all the college staff in a series of meetings."