The facility, backed by Scottish Government funding of £800,000, will be located in Pollokshields and house 200 pupils.
Work on the new school will begin in September and is due to finish in early 2015.
It is part of a five-year Government plan to revitalise the language.
Alastair Allan, Minister for Learning, said: "I am delighted to announce this latest funding and look forward to work beginning on the school to create an environment that will inspire pupils and school staff throughout their time there."
Glasgow City Council's executive member for education, Stephen Curran, said the money allocated for the new school was "very welcome".
According to the 2001 census, more than 92,000 people in Scotland – just under 2% of the population – had some Gaelic language ability.
Almost half of these people lived in the Western Isles, Highland or Argyll and Bute.