Sir Robert McAlpine is understood to have picked up the £130m Milton Court tower job for Heron Properties.
The contractor is thought to have entered into exclusivity arrangements with the developer, with a full announcement due in 3-4 weeks.
The McAlpine bid is understood to have come in at just over £130m.
There have been rumours in the market that McAlpine had won for the last few months, but the developer always insisted that those suggestions were jumping the gun.
Cnplus.co.uk understands that up until the end of last week Heron was clarifying the terms of a fixed price deal with both remaining parties going for the job – Mace being the other finalist. But it has now entered exclusive negotiations with McAlpine.
Brookfield and Galliford Try had been eliminated at an earlier stage.
Mace and McAlpine have been going head-to-head on a number of big London jobs that have been awarded recently. Mace was today thought to have picked up the New London Bridge Place job, sometimes known as the Baby Shard, and won Park House too, while McAlpine won Selborne House for Land Securities.
The job is to build a 36-storey, 284-apartment residential tower, known officially as The Heron, which will be located on Silk Street adjacent to the Barbican Centre.
The ground floors of The Heron will also be the new home of the Guildhall School of Music & Drama featuring a 608-seat concert hall, a 227-seat drama theatre, and a 126-seat studio theatre.