In what it believed to be a first case of its kind, the licence condition has been applied to Decantus on Grey Street and the Grey St Café Bar and Grill on Grey Street and Market Street.
The council said the stipulation has "been agreed as a condition in order to maintain standards and to keep the street as the city’s premier street".
"This initiative by the city council, with the full cooperation of the applicants, is designed to maintain the quality of the city centre, control crime and disorder and improve health. It also seeks to end the availability of the most irresponsibly priced alcohol by controlling multi-buy promotions which lead to irresponsible drinking.
"This initiative is not about stopping the sensible, responsible drinking which supports pubs as part of the community fabric, creates thriving town centres, and provides employment and growth. The measures are targeted explicitly at reducing harmful drinking and minimising nuisance to residents."
Cllr Henri Murison at Newcastle City Council said: "Newcastle is leading the way nationally on this issue and many other councils like us with a world class night life and destination to manage will follow in our footsteps. Government should take our lead by doing what they can to be tougher on the supermarkets, who have caused the crisis of low cost binge drinking. Only they can tackle this problem."
Legal expert Peter Coulson told the Publican's morning Advertiser sister title M&C Report that the legality of the move is "questionable". He said the decision could be subject to judicial review.
"It’s price fixing and they are not allowed to do it. I think the Competition Commissioner would be interested in this."
He pointed out that minimum pricing agreements have operated in some areas under agreement with operators and authorities but not with such licence conditions. Coulson said he did not believe that the operators could be subject to legal action because of the nature of the licence condition.
Graeme Cushion at Poppleston Allen said the move is "legally questionable to say the least".
He pointed out that the £1.25 figure far exceeds the 45p level being proposed by the Westminster Government, or the 50p rate being pursued in Scotland. These are primarily targeted at discounts in the off-trade.
In November the European Commission sent a nine-page legal opinion to the British Government warning that minimum prices are illegal, and said that the Treasury should increase duty on alcoholic drinks if it wishes to raise the price.