The contractor will deliver 100 Embankment, the second and final phase of the Embankment scheme in Salford.
The nine-storey building is set to provide 166,000 sq ft of BREEAM Excellent, Grade-A office space.
The construction will be located next to its sister building 101 Embankment, which is the headquarters of Swinton Insurance Group.
Work on the project is set to begin immediately, with completion scheduled for early 2020.
Ian Fleming, regional director at BAM Construction, said: “We are extremely pleased to be selected as construction partner to deliver 100 Embankment on this historic city centre site.
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“Our deeply embedded collaborative culture and technological skills mean we are ideally suited to creating a building with a sustainability rating of BREEAM Excellent.
“It is equally important that we are able to add social value, working with local supply chains and assisting with life opportunities such as apprenticeships.”
Tristan Capital Partners, Ask Real Estate and the Richardson Family have secured a forward-funding agreement with Salford City Council.
Paul Dennett, city mayor of Salford, added: “The announcement that BAM is in place to drive forward the delivery of 100 Embankment means we can start to focus on securing an occupier which will deliver hundreds of additional jobs which is great news for the city of Salford.”