Wunderman already works with the Xbox parent company, Microsoft, as its global lead agency for relationship management.
Twofifteenmccann, Xbox's global creative agency of record, is not affected by the appointment.
Wunderman UK is understood to have hired around 12 new members of staff to work on the business.
The agency has been tasked with creating work on a variety of platforms, as well as adapting campaigns devised in the US. A significant portion of the work will be digital, but the brief could also include TV campaigns.