The extra hour, available to about 225 premises, is expected to be in place before the end of the year and brings the city into line with Edinburgh and Aberdeen.
Licensing bosses say the 1am plan is due to changing socialising habits.
The pubs being offered the extra hour will be within the area bordered by the M8, the Clyde and High Street to the east, with the expectation not all will take up the offer and those that do mainly on a weekend-only basis.
Glasgow is also planning to scrap the seven areas designated as 'over-provision zones', essentially areas - including parts of the West End and city centre - considered at saturation point with licensed premises.
Instead, it has designated new areas across the East End and South Side using data on the volume of licensed premises, alcohol-related hospital admissions and crime statistics, as well as the multiple deprivation index.
Other proposals out for consultation include relaxing the 10pm curfew for outside drinking at venues.
But early morning licences for pubs claiming to serve alcohol to shift workers and market traders, providing it is served with a meal, are out.
The handful of nightclubs outside the city centre face being given an extra hour's opening.
'Hybrid premises', which operate as bars and are permitted to stay open until 3am, face, if they provide entertainment, being tightened up.
Casinos offering an after-hours club with alcohol served until 6am face a clampdown.
Malcolm Cunning, chairman of the Glasgow Licensing Board, said: "We regard 1am opening for city centre bars as a sensible compromise for those who wish to stay out a little later but who do not want to go on to a nightclub to do so."
Dr Evelyn Gillan, chief executive of Alcohol Focus Scotland, said: "We fully support the board's proposals to cap the number of licensed premises in areas of over-provision and its recognition that alcohol causes real harm right across the city.
"Reducing the overall availability of alcohol by reducing the number, capacity and opening hours of premises is an effective way of protecting individuals, families and communities from alcohol harm."