Robertson Construction will carry out the work on the building in the village of Portree, with completion expected late 2017.
Skye Councillor Drew Millar announced the contract at the first meeting of a new Highland Council area committee dealing solely with issues on the island.
Completion of the project would see the local authority deliver two standaline Gaelic Primary School in Portree and Fort William within two years of each other.
Councillors added that they would complement Scotland’s other Gaelic schools in Inverness, Glasgow and Edinburgh.
Mr Millar said: “The Portree Gaelic Primary School will be a great asset to the Gaelic community across the west Highlands, and it will help to sustain and progress Gaelic Medium Education on the island.
“This announcement is a great step forward which will be welcomed by the parents who for many years have campaigned for a stand alone Gaelic school in Portree, and I look forward to work starting on the new school.”
“I have absolutely no doubt that the new standalone school in Portree will prove a great success and nurture many more Gaelic speakers.” The contract is part of an overall capital investment programme of £14.8 million in Portree which also includes the formation of a new access road to the school, refurbishment of the former Elgin Hostel building to create a new pupil residence at Portree High, and the demolition of the former Boys’ and Margaret Carnegie residence buildings.
The Scottish Government has contributed £4.75 million to the school project.
Construction work on the new school will commence later this year and the building will open in late 2017.
The actual programme dates will be confirmed once a meeting has taken place with the contractor.