The 50 to 80 access points will be installed in high footfall areas and transport hubs around the city.
The first phase coincides with the Glasgow 2014 Commonwealth Games. A second phase will be rolled out citywide in early 2015.
There will be free 24-hour access to the network for the first six months and after that there will be free access for 30 minutes per day per handset.
Gordon Matheson, leader of the council, said: “Glaswegians and our visitors will soon be able to access multimedia information on the city, its events, businesses and services on their devices.
“This network will play a key role in Glasgow’s transition to becoming a digitally connected, smart city, with all the economic and social benefits that brings.”