The work will begin almost a year after it secured planning permission, according to the BBC.
Abstract (Glasgow) Ltd, who is developing the site, said its on-site works would start within the next few days, after completing the purchase of 303 St Vincent Place.
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Planning permission for the 12-storey St Vincent Plaza was granted in February 2012, and when completed, will house around 2,000 members of staff.
Mark Glatman, Chief Executive of the Abstract group of companies, said: "We are delighted to confirm our move to start construction.
"We have been working hard over recent months to finalise various complex agreements to enable this work to commence and we are very pleased to be able to now move forward without any further delay."
Around 250 construction jobs are expected to be created by the project, with work finishing in early 2015.
(JP/MH)
