The 87-year-old died on Thursday at his East Legon residence in Accra.
The news was confirmed by a family spokesperson who indicated that funeral arrangements will be announced later.
George Benneh is survived by his wife, Adelaide Mary Benneh, six children and several grandchildren.
The Professor served as Minister of State in the SMC2 regime, the AFRC regime and in the 3rd Republic.
He also held portfolios including Lands and Natural Resources, Fuel and Power and served as Minister for Finance in the Limann Government.
He was also awarded the “Star of Volta” by President John Agyekum Kufuor and is also a Papal Knight of the Catholic Church.