Mace will be main contractor on the £140m scheme under a design and build contract for the site which was formerly occupied by the Canadian High Commission.
Work will include reconstruction and restoration of the façade of the neo-Georgian building which has been dismantled brick by brick.
More than 2,000 pallets of stone and brick were removed and transported to a secure off site location for storage during the deconstruction process.
Mace will start construction work this Autumn once specialist contractor McGee has completed piling and excavation of the site.
Pranav Goel, co-head of Lodha UK, said: ““Mace has a very strong track record of delivering high quality, iconic developments in central London.
“No. 1 Grosvenor Square will be one of the most sought-after residential developments in the world and we look forward to working with Mace to deliver this exceptional scheme.”
Gareth Lewis, chief operating officer of construction at Mace, said: “Whether we’re refurbishing or converting older properties, including listed buildings, or delivering new build developments, we are committed to raising the quality of living both in the UK and abroad.
“We look forward to working closely with Lodha to bring their plans for No.1 Grosvenor Square to fruition.”
The original building was constructed in the 1930s and was previously occupied by the US Embassy between 1938 and 1960.
No. 1 Grosvenor Square is one of two residential projects that Lodha UK is developing in London and is scheduled to complete in 2019.
Lodha UK purchased the Mayfair site in 2014. Full demolition including the existing basement is expected to complete in April.
The firm’s other project, Lincoln Square, is located in the heart of London’s legal quarter and is due for completion in early 2019.