The agency, which has handled above-the-line work for Lloyds TSB since 2002 and Bank of Scotland since 2009, picked up the account without a pitch.
Factor 3 and Razorfish were the previous incumbents on the business.
Cheltenham & Gloucester plans to spend £2 million next year to promote its core product range of mortgages and savings. RKCR/Y&R will be responsible for all Cheltenham & Gloucester marketing activity.
MEC will continue to oversee media planning and buying, while Rufus Leonard, the brand consultancy, has been appointed to handle design and in-store communications.
Eithne Anderson, the head of marketing communications for Cheltenham & Gloucester, was responsible for the appointment.