The builder beat rival bids from BAM, Kier, Mansell and Morgan Sindall to secure the job to double the size of the existing library building, initially expected to cost £11.5m to build.
The redevelopment will involve the complete refurbishment and overhaul of the existing library, this will include a complete new facade.
This cladding will be continuous around both the new and refurbished element to ensure it acts as one building.
Hopkins Architect designed the building with Arup as structural and services engineers. Faithful & Gould are acting as project manager and Turner & Townsend are cost managers.