The move follows campaigners' calls for more funding to plug a funding gap estimated to be £800m this year, rising to £1.6bn by 2021.
The "national crisis" has left councils across the country unable to meet their statutory obligations to children who need extra educational support, according to the claimants in a judicial review brought against the government.
In June, the National Education Union released findings showing that 8,587 children and young people with SEND are currently classed as "awaiting provision" for a school place, and have no access to any type of educational provision.
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Prime Minister Boris Johnson made the funding announcement on Friday (30 August) as part of a wider £14bn schools funding pledge over the next three years.
Anntoinette Bramble, chair of the children and young people board at the Local Government Association, said: "It is great that the government has acted on the LGA's call for a significant funding boost for services that support children with special educational needs next year.
"This funding will help councils meet unprecedented demand for SEND support next year and ensure our most vulnerable children get the support they need."
The National Children's Bureau also welcomed the news, but noted that the pledge comes at an uncertain time, "when promises made today may fall by the wayside as the wheel of fortune turns in Westminster".
The statement called on the government to address other social factors.
"After a decade of austerity, we still need a wider commitment from government to shore up other parts of the system buckling under pressure," it said.
"We need investment in public health and the early years so that parents can give our children the best start in life.
"We need properly funded child protection services so that our children can be kept safe from abuse and neglect. We need an end to the welfare policies that are driving an ever-increasing number of our children into appalling poverty.
"We will watch carefully as the detail underpinning the funding announcements emerge and urge policymakers to be mindful of the parlous state that the nation's schools, services and other support have fallen into."
Meanwhile, a judge is expected to publish his ruling this autumn, following the legal review of the government's decision-making over SEND funding.
The case was brought by three families who say that the government has failed to increase funding for high needs in line with rising demand.
However, the government's announcement is not thought to affect this case.