The contract is part of the £106 million Middlesbrough Building Schools for the Future programme to transform eight schools.
Financial close with Middlesbrough Council is expected to be reached in November.
Two new schools will be constructed under the deal - one to replace the existing Acklam Grange school and the other to co-locate Ormesby and Priory Woods schools.
It was appointed on the BSF programme under the academies framework and aims to negotiate the rest of the BSF schemes next year.
Work is the new Acklam Grange school is expected to start in November, while work on the new school for Ormesby and Priory Woods will start in January next year.
The company wants to agree contracts for the remaining schools under the programme in 2009.