Going forward, the price of a 500ml beer (at 4.3pc alcohol) will be set at a minimum of €1.70, and wine (750ml, 12.5pc), will cost at least €7.40 per bottle. A 700ml bottle of spirits with 40pc alcohol will cost a minimum of €22.09.
The minimum price is set by reference to 10c per gram of alcohol.
The move comes at a time of the highest inflation in 20 years, with reduced disposable income for almost all households.
Drinks Ireland pointedly called for the operation of the new minimum prices to be reviewed after a short time in operation.
Meanwhile it emerged that some retail outlets may have been applying the new rules from January 1 for administrative convenience.
Alcohol Action Ireland welcomed the introduction of minimum unit pricing (MUP), saying it marked a historic development in public health alcohol policy, which sought to address "Ireland's profound difficulty with alcohol use".
The legislation was first piloted by Tánaiste Leo Varadkar when he was health minister but became bogged down in years of debate.
"With almost two-thirds of all alcohol use emanating from off-trade retail sales, the availability of such volumes of cheap drink in every community in Ireland has to be tackled if we hope to address the chronic level of alcohol-related harm that demands so much of our health services," said Alcohol Action Ireland chairman Professor Frank Murray.
"I have no doubt that MUP will prove to have saved many lives."
Drinks Ireland noted that the responsibility for implementing the new law rests with retailers. However, it added: "As with any new public health intervention, there will be a need to review and evaluate this policy measure for effectiveness after a period of implementation."
There has been a mixed reaction politically.
The People Before Profit party said: "We are opposed to minimum unit pricing, as it will not do anything to address the underlying social causes of alcoholism.
"There is also the issue whereby the revenue raised will not be ring-fenced for addiction or health services."
Labour's health spokesperson Duncan Smith, however, said: "Alcohol is linked to the deaths of three people every day in Ireland, so Labour accepts the evidence for minimum unit pricing.
"This change is an important way to try to limit the damage caused by cheap alcohol and it is projected that within 20 years up to 200 lives a year will be saved."
The introduction of MUP for alcohol has been introduced by the Government as part of the Public Health (Alcohol) Act.
Health Minister Stephen Donnelly said: "Today Ireland joins a small number of countries in the world to introduce minimum pricing. This measure is designed to reduce serious illness and death from alcohol and to reduce the pressure on our health services.
"It worked in Scotland and I look forward to it working here."
Scotland was the first country in Europe to introduce MUP in 2018, where it withstood legal challenges, followed by Wales in 2020. The Russian Federation has a legal minimum price, as do regions of Australia and Canada."
Modelling suggests there can be a fall of alcohol consumption across the whole of population of 8.8pc by establishing the new rate of a minimum 10c per gram - yet State revenues will be strengthened, if anything.
It is estimated there are three alcohol-related deaths in Ireland every day.