The road has been restricted to a 17 tonne weight limit since 2001.
It had been hoped strengthening work would be carried out back then, but a lengthy wrangle erupted between Network Rail and the city council over who owned the bridge and the restrictions remained in place.
The row was only resolved in 2006 when it was agreed Network Rail was the legal owner.
But while the transport body owns the bridge and is legally obliged to ensure it can carry a certain weight of traffic, it is not obliged to bring it up to the standard the council insists on for a busy road.
Eventually, Network Rail agreed to pay around £4.3m of the cost of work and the council the remaining £1.7m
The bridge, built in 1877, carries Cathedral Street over the railway lines in and out of Queen Street station, and supports the end of the roof of the station, which is an A-listed building.
Access to Buchanan Galleries car park will be maintained throughout the work and pedestrians can continue to use the bridge.
Motorists will be diverted to North Hanover Street, Killermont Street and West Nile Street but council bosses warn delays are expected, especially during rush-hours.
Archie Graham, executive spokesman for the Commonwealth Games, said: "The bridge is a crucial part of a major east-west route through the city centre and the restrictions have been a serious inconvenience.
"Working without the bridge has pushed a lot of additional traffic through Nelson Mandela Place and George Square and, without investment, the structure would eventually have deteriorated to the point where we would have been looking at a complete closure – even to pedestrians.
"We are providing £1.73 million of capital funding to ensure Network Rail's bridge is not only made safe for the future – but strengthened to a degree where it can be brought back into the road network."