Scottish Education Secretary Fiona Hyslop said the year-long, £5m pilot scheme, involving 35,000 pupils in Glasgow, West Dunbartonshire, East Ayrshire, Fife and the Borders, was a success.
The pilot also reported that parents and teachers were positive about the scheme, while some pupils enjoyed trying new foods.
"This government has made it a priority to help children in their early years and this initiative does just that, providing every child with a free school meal in their first years at primary school," said Ms Hyslop.
The Scottish Government has already published guidance to help school catering staff produce healthy meals.
According to Labour, the education conveners of several local authorities - including North Lanarkshire, East Dunbartonshire, Edinburgh and the leader of Inverclyde Council - raised concern over whether they could pay for the service, with some saying they would have to make cuts to fund it.
But Cosla president Pat Watters told BBC Scotland there was £40m in the budget to provide free school meals to primaries one, two and three.
He added: "There is no reason why anyone should have to cut anything to fund this. This is a government funded project."
Labour education spokeswoman Rhona Brankin also raised concerns about the funding, adding: "Local authorities are already struggling to employ newly qualified teachers and reduce class sizes, but some schools can't even afford photocopying."
Liz Smith, of the Scottish Tories, questioned whether a blanket free meals policy would target the right pupils, while the Liberal Democrats' Margaret Smith said ministers had "failed to make the case" that the plan was the best way to tackle poor diets.
But John Dickie, head of the Child Poverty Action Group in Scotland, said the announcement was "a massive step forward" in the campaign to ensure healthy meals for children, whatever their home circumstances.
"It will help boost children's health, education and wellbeing and provide a really welcome benefit to hard pressed families across Scotland," he said.
A two-year free school meals pilot in primaries is due to start in England next year, while the Welsh Assembly administration said it was currently focussing on improving nutritional standards.
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