The spiral-shaped footbridge was planned as a pedestrian link between Anderston and the city centre.
It was meant to connect to the Anderston Centre shopping and office complex but the second phase of the site was never built.
As a result work on the bridge stopped around half a century ago leaving it ending 40ft above what is now the car park for the Marriott hotel.
But money has now been found to finish the bridge and create a new pedestrian and cycle route.
The bridge will link into a dedicated cycle lane on Waterloo Street, which will also be built this year.
That will result in a cycle route starting at Kelvingrove Park which will eventually run across the city to link up with Central Station.
The £1.7 million scheme is part of a national project from Sustrans, a charity which is creating new cycle and wmore than 75 UK communities.
Work is expected to start this spring.
As well as completing the bridge, the existing bridge will be refurbished and a new ramp created at the Argyle Street end, which will allow access for people in wheel- chairs.
Anderston/City councillor Philip Braat has welcomed the decision to complete the bridge.
He said: "The main reason for wanting to see the bridge completed is for safety and because it will provide a badly needed route to the city centre.
"Since the M8 was put through Anderston in the 1960s there has been a link missing between the area and the centre of the city.
"Anderston has become more and more isolated from the city centre and the completion of the 'Bridge to Nowhere' will bring the two communities together again.
"I want to see the 'Bridge to Nowhere' become a Bridge to Somewhere."
A spokesman for Glasgow City Council said the 'Bridge to Nowhere' project was being funded by Sustrans and the Landfill Communities Fund.
At this stage, the procurement process has not concluded and no award has been made, so the final costs have not yet been thrashed out.