The Enquirer understands that John F Hunt has won the prized package to bring down Elizabeth House next to Waterloo Station.
Demolition work will pave the way for main construction to start on a 1.2m sq ft scheme by developer HB Reavis.
Elizabeth House will be replaced by a new office and retail complex designed by architects AHMM including a 31-storey main tower.
Most big names in demolition are understood to have pitched for the job.
A source close to a losing bidder said: “A lot of firms were keen to get this one but it looks like Hunt have been successful.”
HB Reavis and John F Hunt declined to comment.