The design was chosen by a panel that included people from Hathershaw and Fitton Hill, where the centre will be built, and an RIBA architectural adviser.
The RIBA also launched two other design competitions this week. Expressions of interest have been invited for architects to join a team of consultants to carry out a conservation plan for Lowther Castle and gardens in Penrith, Cumbria.
The second competition, organised on behalf of the Newham council in east London, is for part of the regeneration of the Brooks estate in Plaistow.
The council wants one architect to plan the refurbishment of low-rise housing on the estate and a second to design the refurbishment of two tower blocks.