Under the proposals, which it is estimated could cost the city between £8 million and £10 million, the east and west sides of the square would be extended, subsuming the roads.
It would leave the north and south sides as the only parts available to some authorised traffic.
Responses to a consultation were put before the Neighbourhoods, Housing and Public Realm City Policy Committee on Tuesday.
A survey of 2,267 people found they would like to see more of a public focus on the square, where there could be the possibility of green space and somewhere to relax.
The project would be delivered after 2023 - when the square will be used as the venue for a major cycling championships - with work on the first phase starting in 2020 as part of the wider Avenues project being undertaken by the local authority - which has already led to changes in Sauchiehall Street.
Council leader Susan Aitken said: "The consultation findings echo what our citizens routinely tell us, that something clearly has to change with George Square.
"I'm really encouraged that there is consensus on many key elements.
"The public conversations we have facilitated tell us our people want a greener square with less traffic, a space of high design quality and which continues to function as it traditionally has done, as a space for Glaswegians to gather.
"Our task now is to respond to that, respecting the square's history and place in Glasgow life whilst delivering a civic space which is both attractive and cherished and reflects our status as a European city."
Plans have also been laid for changes to Miller Street to the south and Hanover Street to the north of the square, providing pedestrian accessibility.