The scheme, which is part of a series of road improvements ahead of the Commonwealth Games, will also affect the Clydeside Expressway and traffic leaving the M8 at junction 19.
Roads bosses say the timing of the work has been planned to minimise disruption and delays for people attending events at the SECC and the Hydro.
The works will require roads to and from Anderston Cross to be closed between 10pm on Saturday and 10am on Sunday.
Alistair Watson, Glasgow City Council's land and environment spokesman, said: "This investment in upgrading the traffic signals at Anderston Cross is another important step in rolling out improvements across the city.
"We have spent £45million extra on roads over the last three years and are scheduled to spend an additional £40m over the next four years.
"This investment will enable us to modernise the signals in the area and have been planned so as to cause as little disruption as possible."
Diversions signs will be put in place but drivers are being advised to allow extra time for their journeys.