The five schools, which will provide 500 new places across Yorkshire and the Humber, will have the capital costs paid for by the Department for Education but day-to-day revenue costs picked up by councils.
Nationwide, a new school will open in every English region, including 37 special free schools and two alternative provision free schools. The Department for Education says this will create about 3,500 new places and boost the choice for parents.
Applications will now open in the 39 successful areas to find providers to run the schools.
The schools will provide specialist support and education for pupils with complex needs such as autism, severe learning difficulties or mental health conditions, and those who may have been or are at risk of being excluded from mainstream schools.
Education Secretary Damian Hinds said: “That’s why we are investing significant funding into Special Education Needs units attached to mainstream schools and in additional support so children with education, health and care plans can access mainstream education.
“But we recognise some children require more specialist support. These new special free schools and alternative provision schools will make sure that more complex needs can be provided to help support every child to have a quality education.”
A free school is a non-profit-making, independent, state-funded school which is free to attend but which is not wholly controlled by a local authority.
In Hull, the free school will provide an extra 125 places for children with severe learning difficulties to study in a specialist educational environment.
With population growth there has been a rise in demand for places from children with severe learning difficulties, but the new school means Hull will have sufficient places for all such pupils who need specialist provision.
In Sheffield, Coun Jayne Dunn, the city council's Cabinet Member for Education and Skills, said: “What fantastic news for Sheffield that we are to benefit from a new special school for children with special educational needs and disabilities (SEND).
"We have argued long and loud about the impact budget cuts have had on our young people, but this is positive news. The addition of this new school will have a great impact on many children and young people across the city, providing a broader range of local provision."