The bridge was built over the M8 in the 1970s but left unfinished for 70 years.
It currently ends in mid-air over the Mariott Hotel car park.
The £1.3m completion of the bridge will be carried out by Scotland-based company Raynesway Construction.
Managing director Stephen Scott said: "It is a real honour to complete the missing link and a little piece of Glasgow's history."
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Archie Graham, the city council's executive member for the Commonwealth Games, said: "It is fantastic that the famous Bridge to Nowhere is finally set to be completed. We hope the new route will prove pivotal in transforming cycling in Glasgow and form a lasting legacy following the Commonwealth Games in 2014."
Work on the bridge was funded through a publicly-decided lottery vote five years ago, as well as receiving contributions form Sustrans, a charity that aims to cut travel by car.
John Lauder, national director of Sustrans Scotland, said: "Sustrans and our Connect2 project are all about allowing people to get to where they want to go under their own steam. We are delighted to see work on the bridge begin and look forward to the opening of a vital link in Glasgow's transport infrastructure."
The M8 will remain open throughout the construction project, as work will be carried out from an enclosed gantry.
(NE/GK)
