Brookfield and Mace will go head to head for the 247,354 sq ft development, which is understood to have a construction value of over £100m.
GPE formed a joint venture in 2013 with the Hong Kong Monetary Authority to develop the project, located next to Bond Street station.
As part of the deal, GPE transferred the properties forming part of the estate to the JV, known as the GHS Limited Partnership, for £202m.
GHS will also acquire the long-leasehold interests in the new station element of the site from Crossrail, once the construction of the station structure completes later this year.
In total the project will include six luxury residential flats and a mixture of office, retail and restaurant space.
Works will include the construction of two new buildings along with the refurbishment of the listed 20 Hanover Square building.
GPE is largely focused on development in the West End and is undertaking a major regeneration of Oxford Street. It also has a number of other schemes in development in the City and south London.
Last July, Construction News revealed that Wates was set to bag a 97,800 sq ft refurbishment job at 148 Old Street with the developer. GPE obtained vacant possession on site in May and had a target completion date of early 2017.
The client is delivering the refurb through the Great Ropemaker Partnership, a 50:50 joint venture with the BP Pension Fund, which acquired the project for £30m from the BP Pension Fund in April 2013.
Brookfield Multiplex and Mace declined to comment.