The contract award follows its completion of the £23m main school complex, which opened in 2018.
Work on the new two-storey classroom block is expected to start in April and will provide a further 240 places at the school in Hadfield, near Glossop.
Ian Taylor, managing director of Henry Brothers Midlands, said: “The new development will nestle into an existing bank on the south side of the school and will be accessed via a covered walkway into the top floor, with an outdoor stairway down to playgrounds and fields below. Henry Brothers Midlands is looking forward to starting work on site to provide additional facilities and space for this popular school.”
The building design has been developed by DLA Architecture jointly with Derbyshire County Council and the school. The project is being funded by Derbyshire County Council.
It is expected that the new block will be completed in spring 2022.
The Henry Brothers Midlands team on the project includes DLA Architecture, civil and structural engineer Curtins and Couch Perry Wilkes for M&E services.
As well as building the main complex at Glossopdale School, Henry Brothers has also done external works on the site, including developing sports pitches.
Elsewhere in Derbyshire the company is also building the new £13.2m Alfreton Park Community Special School.