Most recently, he founded the digital agency Big Picture, whose clients include Halifax, STA Travel and Tetley.
Andrews, who starts his role at the end of October, will report direct to GroupM's chief strategy officer, Nick Emery.
He will be working in a network of 96 offices in conjunction with MindShare's other digital group heads: the worldwide chief executive, John Montgomery, the EMEA chief executive, Rob Noss, and Ruth Stubbs, the chief executive of GroupM Asia-Pacific.
Emery said: "In a market full of hype and inexperience, Andrews is a bloodied and pedigree talent who will continue to ensure that digital is at the centre of our strategy."
Andrews joined DLKW in 2000 - at the time of its management buy-out - and helped to develop the agency's capabilities in digital, direct and integrated marketing.
Andrews was also one of three partners who launched Poppe Tyson, the interactive marketing agency, in 1996.
He said: "To help shape how MindShare adds value for its clients is irresistible. I'm looking forward to working with the team to deliver groundbreaking work."
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