The scheme, which is endorsed by Strathclyde Passenger Transport (SPT), will now be subjected to detailed feasibility assessment by consultant Grant Thornton.
"The city needs a world-class subway system, but l realise an extension will not come cheap, and we still have lots of hurdles to overcome," said SPT chair Cllr Alistair Watson. "However, we have the prospect of the Commonwealth Games in 2014 and will need to move large numbers of people around the city safely."
The new railway would use a disused tunnel between Bridgeton and Parkhead and a viaduct between the city centre and the exhibition centre. These have received care and maintenance since the 1960s closures and were found to be structurally sound by recent inspections.
The line would be connected by interchange beneath Argyle Street in the retail core to the existing rail and subway networks.
In contrast to reaction to an earlier proposal for a new eastern circle subway route with a price tag of more than £3bn, locals have embraced this plan.