The job known as Alpha Place is one of the last prime sites in Chelsea, just a few hundreds yards from the Thames and King’s Road.
McAlpine will build 38 luxury flats with ground floor gym complex and extensive underground car parking on the cleared site, which was previously a electricity transformer station.
Work on the two-year job is expected to get underway next month.
The firm’s London team is also stalking another landmark residential scheme in the capital.
Developer Almacantar has confirmed that it is in talks with the contractor about plans to convert the 34-storey Centre Point office tower in London into residential flats.
The developer with partner Frogmore Estates has submitted the proposal to convert iconic tower from mixed-use to 82 luxury flats next month.
The huge refurbishment will not see any part of the iconic grade-II listed tower demolished.