Balfour Beatty, Mace and Sir Robert McAlpine are among the firm shortlisted for the building contract, estimated to be worth as much as £160m. A winner is expected to be named next month.
Enabling works have just been awarded to McGee and will run until April.
The 3-acre site was once to be developed as NoHo Square, because of its location to the north of Soho, by the Candy Brothers but stalled.
Under the new plan, the big West End brownfield site will be transformed into an mixed-use community, centered on a landscaped public square containing the listed hospital chapel.
The development will consist of two 9 to 11-storey buildings for mixed use purposes.
Together they will house 291 homes, around 200,000 sq ft of offices, 20,000 sq ft of retail and restaurants.
Neighbouring Camden Council had called for the scheme designed by Lifschutz Davidson Sandilands and Sheppard Robson’s to be rejected on the grounds that it was incongruous with the local area.
Mark Younger of Exemplar said: “We are delighted that Westminster City Council has approved our plans for the former Middlesex Hospital site, as it is one of London’s most important development opportunities.
“With enabling works underway, we are already bringing this vacant site back into use and anticipate strong demand for the offices, retail units and apartments once we begin marketing later this year.
He added: “We will continue to work closely with local residents to ensure that the chapel and other community spaces provided within the scheme are fully utilised to benefit everyone in the surrounding area.”