Mr Dolman joined Christie's 26 years ago and has been CEO since 1999, prior to which he was managing director of Christie's Europe and of Christie's Americas and Christie's Amsterdam.
Mr Murphy comes to Christie's having held several senior executive positions in the media industry, including, most recently, CEO of Rodale Inc.
Prior to that he was executive vice president and managing director for Disney Publishing.
Both will report directly to Patricia Barbizet, CEO of Artemis, Christie's parent company. Mr Dolman will focus on business development and client relationships at senior level while Mr Murphy will be responsible for the overall strategy and management of all the company's operating units.