The new school will have space for 140 pupils, and will be located next to St Nicholas Primary School, on Kitwood Road, Skirbeck.
The John Fielding School will relocate to the new facility, which will be named Boston Endeavour Academy.
Cllr Mrs Patricia Bradwell OBE, executive councillor for children's services, said: "This is a very exciting moment as the county council starts to deliver the special school building project across the county.
"There is no better place to start the project than here in Boston, investing £13.2m on the new school building, with an expected opening date of autumn 2021.
"The new school will ensure all children in the local area are able to receive high quality education as near their family and local community as possible."
The new school site will include 16 classrooms, specialist teaching spaces for science, technology, ICT and art, and a hall.
It will also benefit from a hydrotherapy pool, sensory and soft play rooms and dedicated therapy spaces. Outside, there will be hard and soft-surfaced play areas, as well as a sensory garden and wildlife areas.
Richard Gamman, Headteacher of the John Fielding School, said: “We are all absolutely delighted and excited to be moving to these new state of the art premises. We are looking forward to the additional specialist facilities and larger classrooms, and being able to provide more desperately needed places for the people of Boston and surrounding area.”