The Enquirer understands that Kier has fought-off competition from a series of heavyweight rivals to land the contract from the West London Mental Health Trust.
Other bidders in the race included Balfour Beatty, Skanska, Vinci UK and Willmott Dixon.
The hospital construction contract is believed to be valued around £150m.
A source at one disappointed rival said: “It was a competitive race but Kier put together a very strong bid and the word is they have won it.”
It is understood that Kier’s bid was up to £18m lower than the next cheapest.
West London Mental Health Trust plans to build a new hospital containing 160 mental health beds alongside the existing 1863 Victorian listed buildings.
Construction of the new 10-ward complex at the high security facility in Crowthorne is expected to start in the autumn of 2013.
The Basingstoke office of WSP is main structural consultant.
The redevelopment, designed by Oxford Architects Partnership, will be paid for by the Broadmoor Hospital Trust with some funding coming from the government and from selling off land holdings.
Bracknell Forest Council has plans to use the land for house building and it has already been mooted that the existing Grade II Victorian buildings could be converted into a hotel.