The global leadership position will see Law working alongside Bill Brock, the co-founder and chief executive officer at AnalogFolk.
Law has been tasked with "driving business performance", integrating new global services and helping the company expand into new markets.
He joined the agency in 2011, and was previously a business director at Elvis between 2009 and 2011. Before this he was a group account director at Dare for three years.
Davies’ remit will be to "focus on driving excellence in creativity through innovation" at the London agency.
Brock said: "During Matt’s tenure as managing director, the London office has more than quadrupled in size, and even during this growth we’ve maintained our unique and much-admired culture.
"I’m delighted that this experience will now be deployed on an international level to align with our global ambitions.
"In the six months he’s been at AnalogFolk, Ete has demonstrated incredible leadership skills and unparalleled expertise in service design. He’s a strong cultural fit and the perfect successor, so I’m thrilled he’ll be driving the agency forward in the UK."
Davies left AKQA last year, and has also worked at Tribal DDB, FullSix and Modem Media (now DigitasLBi).
He said: "2016 is shaping up to be a transformational year for AnalogFolk. I’m very proud to be leading the UK offering through this."