The move is the first step in the cost-cutting review instigated by new Elland Road chairman Professor John McKenzie after the club revealed debts of almost £80million in March.
McKenzie has now also become full-time executive chairman assuming direct responsibility for all the company's operations.
Harrison became finance director in February 2000 and was promoted to the role of chief operations officer in June 2002.
Neil Robson, a director of Ernst and Young LLP, becomes chief financial officer until a permanent board appointment is made.
The club has also revealed that an Ernst & Young team, led by Gary Wilson, has been appointed "to advise on alternatives for restructuring and refinancing the company".
The restructuring of Leeds United has begun with the resignation of troubled soccer club's finance director Stephen Harrison.
