It also got the green light to build a new male medium secure unit at St Bernard’s Hospital in Ealing.
A formal contract signing with the West London Mental Health Trust will now take place later this month.
The Broadmoor new hospital has a construction value of the projects is £115m, substantially less than the original £150m construction cost estimate, while the Ealing secure unit will cost £43m to build.
Work will involve construction of a new Broadmoor hospital, containing 162 mental health beds, to replace the facilities currently provided in outdated buildings.
Building works are expected to last three to four years so that the new hospital will be ready to take patients from the beginning of 2017.
Kier St Berhard’s job will see construction of an 80 bed medium secure unit (above) on the existing John Conolly Wing site.
Managing director of Kier Construction’s major projects business, Colin Lamb, said: “This latest milestone is a significant development that demonstrates how successful the collaboration between the partners has been.
“We look forward to working very closely with the Trust to deliver these facilities, which will provide excellent new facilities for the benefit of the patients and the wider communities.”