Adams, a non-executive director, will replace Roger Pedder as chairman on January 31.
Conviviality, which runs Wine Rack, Thorougoods and Select fascias along with 616 Bargain Booze stores, has also appointed Martin Newman and Steve Wilson as non-executive directors.
Newman has 25 years experience at retailers including Harrods, Burberry and Red Baker and will chair the company’s remuneration committee.
Wilson is a fellow of the Institute of Chartered Accountants and is group finance director at Headlam Group. He will chair the firm’s audit committee.
Conviviality’s chief executive Diana Hunter said: “I would like to take this opportunity to thank Roger for his stewardship of the business over the past eight years and wish him all the best. I would also like to welcome both Martin and Steve to the board, who along with David as chairman will work with me to shape Conviviality for the future.”