The Evening Times reported on Saturday that the work was to be carried out and the main road to the Southern General site was closed yesterday so sections of the bridge could be put in place.
The new link is between the Institute Of Neurosciences building and the rest of the hospitals. It means that when they open in 2015 patients and staff will be able to move between the maternity unit, children's hospital, adult hospital and the site's research and learning centres without going outside.
Work began at 7am yesterday as sections of the walkway were transported to the site.
David Loudon, NHS Greater Glasgow and Clyde project director, said: "This will provide a physical connection from the new hospitals to the Institute of Neurosciences and planned Clinical Research Facility and Learning and Teaching Centre."
The hospital complex will cost £842million and when finished it will have 1109 beds and a hi-tech Accident and Emergency department, as well as Critical Care wards and theatres.
Every patient in the general wards will have their own single room with an en-suite.