The project had been delayed after one of the bidders objected to the tender process after BAM was originally awarded the job last year.
West Dumbartonshire Council have now granted the scheme full planning permission and confirmed BAM as main contractor.
Rivals who lost out are believed to include Farrans, Luddon, Balfour Beatty, Barr and Ogilvie.
The application to demolish the existing Dumbarton secondary school is set to go before a meeting of the local planning committee by either January or February.
Construction work is due to be completed by summer 2013.