Education Minister David Laws told BBC News he expected some 15,200 primary schools – or 98% of the total – to be ready to provide the meals.
A small minority of schools will have to provide cold meals as their kitchens are not ready.
Some schools say government money to improve kitchens has not been enough.
Mr Laws congratulated schools on “a truly fantastic job in preparing for this important milestone”.
“Today our goal to offer every infant child a healthy, tasty school meal has become a reality, a move that will put money back in parents’ pockets while ensuring all children get the best possible start in life.”
The government has provided £1bn to meet the costs of the meals, which are available to all pupils without means testing, over the next two years.
The free meals are available to pupils in the first three years of school.
In addition, it has made £150m available to improve kitchen and dining facilities, plus an extra £22.5m for small schools.
Schools will have a legal duty to offer the meals, which are expected to save families £400 per year per child.
Some 1.9m children will be eligible, up from 367,000 previously when free school meals were limited to families on benefits or earning less than £16,190 a year.
Some schools and local authorities have complained the funding was not enough for them to improve their facilities in time.
BBC research suggested some 2,700 schools would not be ready by September .
About 1,700 had no kitchen at all while others had inadequate kitchens and poor dining facilities.
Leaked emails from within the Department for Education suggested some senior officials believed the policy had not been properly costed.
However, Mr Laws said the latest figures suggested most schools were ready.
He said that for the next few weeks some 240 schools could only provide cold meals. Of these, some 50 or 60 would have to delay hot meals until January.
The Local Government Association said that councils and schools had been working “really hard” to make the free school meals for infants happen.
Nick Forbes, vice-chairman of the LGA’s children and young people board, said it was a tribute to councils and schools that this had been achieved in such a short time and with “a lack of funding in some areas”.
“Dishing up a nutritious lunch for every young pupil will improve their experience of school and help them concentrate in lessons. But in some cases money earmarked to repair school roofs is being diverted to plug the £25m shortfall in cash needed to provide free school meals.
“The government, in making this promise, should also have made the money available to deliver it,” he said.
Carrieanne Bishop of the Lead Association for Catering in Education paid tribute “to the thousands of school cooks, caterers, teachers and council staff who have worked hard over the summer months to get schools ready for the start of term and introduction of infant free school meals.
“This is an overwhelmingly positive policy that will bring a whole raft of benefits to schools, parents, teachers and children, now and in future years to come.”
The Children’s Food Trust described the rollout as “great news for children”.
Chief executive Linda Cregan said: “Throughout we’ve been really impressed by the determination, will and enthusiasm of schools to overcome their challenges and offer all their infants a healthy, tasty lunch.”
Deputy Prime Minister Nick Clegg, who announced the free meals plan last year, said said he was delighted to see it rolled out.
Shadow education secretary Tristram Hunt said: “Nick Clegg has over-promised and under-delivered. Many schools have had to raid their budgets to pay for a policy that was introduced on a political timetable.
Mr Clegg has said he would like to see free meals for all pupils up to the age of 11, a policy also recommended by a recent review of school food by the founders of the Leon restaurant chain.