The builder, which is part of the Keepmoat Group, will refurbish the 1960s tower blocks – Montgomery House, Churchill House and Alexander House over four years.
Social landlord One Vision Housing is behind the Kings Park regeneration project, which will see three new storeys on top of the existing apartment blocks taking them to 18 storeys.
Including ground floor extensions more than 109 new apartments will be added to the existing 174 flats.
Bramall’s area director, Steve Parrington, said: “This is a very significant contract win for Bramall Construction as it will help us to enhance our portfolio and track record in high-rise refurbishment.
“We are proud to be working on such a high-profile project which will create attractive homes and will, in turn, help transform Seaforth and bring about improvements throughout the area.”