Cheesman will take the position when Joseph Berkmann stands down as chairman of the company after 40 years in the role.
Deputy chairman Keith Calnan said Cheesman's valuable experience within the wine trade and his many contacts would help to grow the company. "His reputation and standing in the the wine trade is first class and this alone will bring added benefits to the company," he said.
Berkmann, 76, will continue as a director of the company and remain chairman of parent company, Berkmann Holdings Ltd.
Cheesman was wine director at Sainsbury's for a number of years and currently serves on the boards of several organisations in the wine trade, including the Wine & Spirit Trade Association.
Berkmann Wine Cellars first started supplying wine to Joseph Berkmann's chain of London restaurants in 1964 and now supplies both the on- and off-trade from its six branches in the UK.