The city’s licensing board hope the policy will help solve the problem of anti-social behaviour and ill-health associated with binge drinking.
There are about 2,000 pubs and clubs in Glasgow and all are expected to sign up or risk losing their licences.
The licensing board decided last November to end happy hours, but waited until its first quarterly meeting of 2004 to implement the policy.
In return for helping Glasgow become the first city in Scotland to successfully ban happy hours, the board will relax drinking rules and allow city centre nightclubs to serve alcohol until 4am on 12 separate occasions each year.
However, pubs ignoring the policy face losing the right to open until midnight, while nightclubs could have entertainment licences scrapped.
Ultimately, regular offenders could face losing their licence to trade.
Recent figures show alcohol-related deaths in Glasgow have increased to more than 400 a year, 60 per cent higher than the rest of Scotland.
Binge drinking costs Scotland 1.07 billion a year, with about a million workdays lost, while domestic and drink-related violence costs NHS Scotland 95.6 million a year.
Right up until yesterday’s deadline some city-centre pubs were still advertising two-for-one drinks and cut-price offers.
But Councillor Gordon Macdiarmid, chairman of the licensing board, said he was confident most operators would be signing up.
He said: "It has taken us years to reach this point, but the indications are good. I believe most operators are in favour of the ban.
"I am also certain that, once we get past today and tomorrow’s meeting, the policy will be accepted by the first batch of premises whose licences are up for renewal.
"Operators will be required to sign up because there is no point having a policy if it is not underpinned by a sanction like losing their licence.
"Down the line we would hope the policy will lead to everyone in Glasgow being able to enjoy a night in the city without the anti-social behaviour and effects of binge drinking."
However, industry leaders called on the board to clarify quickly what qualifies as an "irresponsible promotion".
Eddie Tobin, of the Glasgow Nightclub Forum, said he fully supported all measures that would rid Glasgow of the scourge of binge drinking, but he added: "There is still a lot of grey area."
Paul Waterson, of the Scottish Licensed Trade Association, added: "I think the new policy will go some way to addressing binge drinking ."
A spokeswoman for Alcohol Focus Scotland said: "Happy hours are nothing short of a blatant invitation to binge drink and get intoxicated, increasing the risks to people's health and safety."