Construction of the £207m line to Newhaven is scheduled to last until summer 2021.
Traffic disruption expected as North Bridge cut down a single lane in each direction from Monday.
Industry leaders believe buses can be part of the solution with a shift from private cars to sustainable transport.
Get Glasgow Moving has received support from thousands of residents since it launched the petition in June.
Sir Brian will remain on the board but his sister Dame Ann Gloag is retiring completely.
The 21-year-old was taken to Ninewells Hospital in Dundee after the incident in Arbroath.