The clampdown will be part of Scotland's first pollution-busting low emission zone (LEZ), which will start operating on 31 December.
Initially, one in five bus journeys in the zone will have to be on vehicles with the cleanest diesel engines - Euro VI.
This compares to around one in ten at present, with a phased approach until all buses meet the standard by December 2022.
BACKGROUND: Dirty engine buses face Glasgow city centre banHowever, no phasing for cars and other vehicles towards the 2022 deadline has been announced.
Edinburgh, Aberdeen and Dundee are also due to launch LEZs by 2020.
Diesel cars will be required to have Euro 6 engines, which were introduced four years ago.
Petrol cars will require Euro 4 engines, introduced in 2005.
Some buses - such as main operator First Glasgow's - have their engine rating shown on a rear corner of the vehicle, which range from "3" to "6", with six the least polluting.
Diesel fumes are harmful to health, with Hope Street, one of the city's main bus corridors past Central Station, among Scotland's most polluted.
She said: "While we continue to work with the bus industry to improve services – services which are vital to the lives of Glaswegians - it’s recognised that the introduction of a LEZ needs to be proportionate and managed in such a way that ambition and practicality can be balanced.
“That is why the initial phase of the LEZ will address local buses through Traffic Regulation Conditions (TRCs) set by the Traffic Commissioner.
"Buses will be expected to meet the Euro VI emission standard by December 2022.
"All other vehicles will also have to be compliant by that date, so we will be engaging widely with residents and businesses to ensure that everyone is aware of and prepared for the LEZ.
“Glasgow is forging a national path towards cleaner air – air that we will all benefit from.
"Poor air quality is a significant public health concern and a major social justice issue for Glasgow.
“Cleaner buses going through the city centre LEZ will also be travelling elsewhere and throughout our city’s neighbourhoods and this is a really positive step forward in how we, as a city and as a country, go about creating healthy, liveable streets.”
However, environmental campaigners accused the council of not acting fast enough.
Friends of the Earth Scotland air pollution campaigner Emilia Hanna, said: “The people of Glasgow were promised a low emission zone, but these proposals will create a ‘No Ambition Zone’ that does almost nothing to speed up air quality improvements so desperately needed in the city.
“The proposals condemn Glasgow to illegal air for years to come and must be urgently improved.
"Councillors must recommend these proposals be significantly improved when they discuss them next week or they will have failed the people of Glasgow, who suffer daily from the health impacts of air pollution.
"What Glasgow does also sets the benchmark for the LEZs to come in Aberdeen, Dundee and Edinburgh in 2020, so it is critical to set the bar high."