It will be built on an old goods yard site, north of Paddington railway station, where there has already been significant development by client Development Securities.
A source at one firm that submitted a bid in May said: 'We never really nailed down who was involved in this. The five firms we thought were Skanska, Laing O'Rourke, Bovis Lend Lease, Alfred McAlpine and Wates.'
Another contractor said: 'As far as we were concerned it went down to Skanska, Bovis and Sir Robert McAlpine.
'But others have said Bowmer & Kirkland was one of the last three. I'm not even sure there was a last three or if it went straight from five to a winner. I don't know why there was all this secrecy.'
Development Securities is expected to formally award the contract in January, with the next few months being used for negotiation. Work will start shortly afterwards for completion in autumn 2007.
The building was designed by architect Sheppard Robson.
Bovis Lend Lease is also in the middle of a £30 million Crossrail deck contract, which is due to be finished next summer, for Development Securities at the same site.
Building 3 is being built speculatively and the client expects to find a tenant easily as previous phases at the site have been let before completion.
It is the first part of new work planned at the site for which planning permission has already been granted.