BAM will convert the 150-year-old buildings into modern offices, studios and dining spaces under the deal with developer the King’s Cross Central Partnership.
Jamie Oliver Group will open a restaurant within the brick arches on the canal-level floor, and on the ground floor.
It will also open a pub in the Western end of the building, with a roof conservatory and an outdoor roof terrace, and base staff in offices and studios on the upper floors.
BAM has just begun work on-site, with completion scheduled for spring 2016.
BAM Construction director Mike Donegan said: “BAM is very pleased to continue its work on this landmark central London development. BAM is behind something like a dozen structures here.
“Our work here for Argent shows how trusted and successful we are at turning the most ambitious and high profile projects into reality for the UK’s leading developers.”