The Barratt subsidiary will work with the local authority to redevelop shops, offices and flats in the Peach Street, Rose Street, Market Place, and Elms Road areas.
Wilson Bowden was selected from a shortlist of three, which also included Gladedale and Development Securities.
The next stage in the redevelopment project is to draw up detailed plans for the sites.
The redevelopment of the Peach Street and Elms Field sites is expected to feature new restaurants, cafes, shops, offices and homes.
Construction work on the regeneration scheme could begin next year.