The new modular two-storey building will feature five science labs on the ground floor as well as four maths classrooms and one graphic communications room on the first floor. New toilets are also being provided.
Work is expected to be completed by October of this year.
The investment is a response to the growing school roll, which has risen to 402 and will increase further to 416 by the start of the new school session in August.
Already two huts which housed four classrooms have been cleared from the school site.
The school is being built in 48 modules off site by Yorkshire company, Britspace, and will be assembled on arrival at the rear of the school building, which borders Grantown Golf Course and neighbours the Craig MacLean Leisure Centre.
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Britspace have also won the contract to build an extension at Nairn Academy.
Head Teacher Mrs Irene Carson said: "I am absolutely delighted that The Highland Council has managed to resolve our serious accommodation problems in such a short timescale.
"The extension will free up space within the existing building and provide us with modern surroundings, more fit for the 21st century."
The Council's four Badenoch and Strathspey ward members on The Highland Council have been working hard with the school management and parent council to press for the extension.
Councillor Jaci Douglas said it was very encouraging to see the school roll increase so significantly as it meant more people were moving to Strathspey and that the area was thriving.
She said: "This is a very exciting project, which promises to bring a significant improvement to the teaching and learning experience of staff and pupils. Situated as it is beside the excellent Craig MacLean Centre, it will also provide Grantown with first class community facilities.
"This new method of construction is a first for the Highlands and it is great that Grantown Grammar is leading the way. Staff and parents have all been campaigning for this new accommodation and full praise goes to them for their hard work in securing this first class addition to the school."
The extension should be completed in the autumn.
(GK/JM)
