The £60million project will transform the site of the old Odeon Cinema building at the corner of Renfield Street and West Regent Street into a modern office block.
In order to carry out the work, West Regent Street from Renfield Street to West Nile Street, and West Nile Street between Bath Street and West George Street, will be closed.
It is expected the closure will begin at midnight and be completed by 6am on Monday.
Nick Berry, a director with joint-developer Mountgrange, said: "We have had two road closures in the past to allow ScottishPower to remove a substation.
"This closure is to allow us to get the machinery in place for the demolition.
"The building is scheduled to be completed by early 2015. At the moment the project is on time and we expect to begin construction work in June."
During the works diversions will be in place southbound via Bath Street, Renfield Street and West George Street and northbound via St Vincent Street, Hope Street and Renfrew Street.
The development is the first new-build of its kind in Glasgow's city centre area in almost five years, and will help tackle an acute shortage of quality, modern office accommodation in the city centre.
Shop units on the ground floor are also planned and construction work is expected to be completed in the run- up to Christmas 2014.
While the developers, Mountgrange and PRUPIM, are doing away with the cinema's red-brick auditorium, the his- toric art deco facade and foyer in Renfield Street are being saved.
Its construction is creating about 130 jobs.
In a separate announcement, Glasgow City Council have said Hope Street – from Renfrew Street to Cowcaddens Road – is to close this weekend from 6am on Sunday until 6am on Monday to allow crane work on the revamp of the Theatre Royal in Hope Street.
A diversion will be in place via Renfrew Street, West Nile Street, Port Dundas Road and Cowcaddens Road.