A trial will take place at one school in early 2024 to provide children there with free school meals.
Westfield Primary School pupils are expected to be given free school meals next year, provided adequate funds are raised.
Only then will further schools be considered for free school meals.
The council will create a fundraising pot to pay for the meals, as pledged in Labour’s manifesto.
Executive member for children, young people and education, Cllr Bob Webb said: “We have made good progress so far in working towards the creation of the ‘York Fund’, a pot of money that organisations, individuals and businesses can contribute to in covering the costs of free school meals across the city.
“We expect the York Fund to be formally established by November, after which it will be publicised and we encourage anyone in a position to contribute to do so.
“We have also formed a working group including external expertise to help develop our proposals, before getting started early next year.”
Before then, the council will progress “an auto-enrolment trial period for free school meals to ensure the government is providing funding for all those who are entitled,” Cllr Webb said.
“From early next year, we plan to trial universal access to free school meals at Westfield Primary School, once funding is in place.
“We will evaluate this trial before planning a wider rollout to the first tranche of schools in communities that need this support the most.
“This is something we want to do as one city to help in the current cost-of-living crisis, with the goal of ensuring all children are fed so they can learn and achieve their full potential.”
Members of the opposition group on the council, the Liberal Democrats, have been sceptical about whether Labour would be able to fund the pledge made prior to the local elections and say it will take £3 million to fund it.
Deputy leader Cllr Paula Widdowson said: “Their first 100 days in control of York council have seen broken promises on universal free school meals for primary children, city centre access and council tax freezes.”