Now the firm can start converting the Grade II-listed building into a boutique hotel, with the court room becoming a restaurant.
Old cells in the basement of the building will be turned into a museum, now the plans have been approved by Westminster City Council.
McLaren is understood to have secured the contract ahead of rival bidders ISG, Galliford Try and Sisk.
The building – which once housed prisoners including Casanova, Oscar Wilde and the Kray twins – will be partially preserved and transformed into a 99 bed hotel.
Work is expected to start this autumn and take around 21 months to complete. Waterman are the M&E consultant on the job.
The building was originally home to the Bow Street Runners – London’s first professional police force which was founded in 1749.
At the moment, artefacts from the Met’s 184-year history are only available for the public to view without appointment at the Metropolitan Police Heritage Centre in Fulham, south-west London.