Dean Oates, 45, pleaded guilty to conspiracy to commit fraud when he appeared before Leeds Crown Court.
Co-accused Peter Alp, 52, entered a not guilty plea to the charge and is likely to face a trial in June next year.
The charges relate to an alleged £178,340 missing from the theatre’s accounts.
Alp and Oates appeared before the court for a brief preliminary hearing where the charges were put to them.
It is claimed Alp, who was head of finance at the historic theatre and had responsibility for the finances of other council-related charities, conspired with Oates to fabricate 54 invoices for services from a company called Bittern Entertainment that were never provided.
The alleged offences took place over a two-year period from 2011 to 2013.
The hearing was adjourned and Alp, of Minster Drive, Herne Bay, Kent, and Oates, of Lime Bar Lane, York, will next appear before the court on January 5.
A 51-year-old woman from York, who was also arrested, remains on bail pending further inquiries.
The alleged fraud came to light after Leeds City Council carried out an audit of the charity’s accounts.
A subsequent audit by Armstrong Watson accountants found computer password breaches had led to the suspected fraud payments being made.