Work is due to start on the shell of the building next month and includes the mammoth task of dismantling and then rebuilding the four chimneys in concrete to the original design.
The painstaking process of cutting down the chimneys will begin in February.
Mace will also oversee the extensive brick repair package of work to the existing shell, which has been left shored up by temporary works for more than 20 years.
The firm beat rivals Sir Robert McAlpine, Lend Lease, Brookfield and ISG to take the package, making it a strong bidder for the £600m main shell and core works for the old power station.
Tenders for this will be invited next year with a start planned in early 2015.
Rob Tincknell, chief executive of Battersea Power Station Development Company, said: “The restoration of the power station is at the heart of this entire redevelopment.
The appointment of Mace, which has an excellent track record in historic and specialised buildings, will ensure that Gilbert Scott’s masterpiece is in safe hands and that all the contractors working on its restoration are pulling together so that we can finally refurbish it and open it up to the public.”