Purser has worked at Iris for a year, leading the agency's digital strategy team and handling clients such as Philips, Volkswagen and Barclaycard.
At M&C Saatchi, Purser will report to Enyi Nwosu, the central strategy unit managing director. Purser will join a team that brings together strategists, planners and market analysts across Lida, M&C Saatchi Sport & Entertainment and M&C Saatchi PR.
Before joining Iris, Purser was the director of strategic consultancy at the digital agency LBi, taking the global lead on its Unilever business and the European lead on Electrolux.
Lisa Thomas, the chief executive of M&C Saatchi Group, said: "Christian has a proven track record of leading multi-disciplinary teams and delivering genuinely integrated digital thinking."