Peter Weir said the Finance Minister Conor Murphy will make an announcement on the matter soon.
Mr Weir bid for money from Stormont’s Covid-19 fund to extend the scheme over the July and August period.
Direct payments for the school meals had originally been scheduled to end on 30 June.
On Friday, he said the Executive has now agreed to it.
“I think there is unanimous support and it is more far-reaching than, for example England.
“We are also backing this up with the Eat Well Live Well strategy, which targets the most vulnerable children out there to make sure they have meals.”
It is understood the current system, where direct payments are put into parents’ bank accounts, will continue over the summer – unlike in England where parents receive vouchers.
On Tuesday, the government in England agreed to extend the scheme following a campaign by footballer Marcus Rashford.
Scotland and Wales had already committed to continue the scheme, leaving Northern Ireland the only part of the UK that had not.
Last month, Mr Weir had said his department could not afford to fund payments over summer.
However, on Tuesday a spokesperson for the NI Department of Education said the minister was “currently considering options to cover the July and August period”.
The families of almost 97,000 children have been receiving payments of £27 every fortnight per child, since schools were closed.
The scheme was introduced on 26 March at an initial cost of £19 million to run until the end of June.
It is estimated that the cost of extending it during July and August could be up to a further £12 million.