Andrews will be responsible for the strategic and creative leadership of the agency, and will run its strategy, invention and insight teams.
He fills a role left vacant since Kim Douglas left to join SapientNitro in early 2010.
Andrews has been at Mother for four years, having previously worked at Vizeum as the head of strategy and joint managing director. His job at Mother was to bring creative media and communications thinking back into the agency following the sale of its stake in Naked Communications to Photon.
He is also a former partner at Michaelides & Bednash, the communications planning agency that was subsumed into Mindshare in 2008.
Andrews said: "It's a fascinating time to be working in media. With technology accelerating the pace of change, the next five years promise to bring even bigger, more dramatic changes to our lives than the last ten."
Jed Glanvill, the EMEA regional director and chief executive at Mindshare, said: "We are delighted that Matt is on his way to Mindshare.
"He has picked up a rare blend of skills and experience on his way, having worked in senior positions on the creative and media sides of the business. We think he'll bring a different perspective."