The Enquirer tipped Kier for the prestigious research centre job in central London last June.
The contractor has now been awarded the job and will start site preparations shortly.
The Sainsbury Wellcome Centre for Neural Circuits and Behaviour will be part of University College London and will be built on a site occupied by the Windeyer Building in Fitzrovia.
The construction element of the building, which will comprise two basements, rising to five floors, is understood to be worth around £45m.
Ian Richie is the architect for the building, with Arup carrying out the engineering design services.