Funds have been awarded by Historic Environment Scotland and will be used to repair the exterior of the building, as well as add office space.
The council then plans to relocate 500 of its staff into the new town centre offices.
The building had fallen into a state of disrepair in recent years after it caught fire in 1976.
Specialist contractors have been hired to carry out the renovation, which includes rebuilding of the roof, conservation and repair of the original stonework, and refurbishment of the existing main entrance timber doors.
The interior will also include a public area and a number of training and meeting rooms.
A large new building to the rear will also be constructed, which will house the new council office space.
Council leader Martin Rooney said: "This is an iconic building at the heart of Dumbarton town centre and I'm delighted that Historic Environment Scotland has recognised the importance of the work we're carrying out.
"In restoring the old Academy building to its former glory, not only will the council bring this building back into use but it will also help provide a catalyst for further regeneration activities in the town centre."
The new building will cost approximately £15.7m, and the council said it will save £300,000 per year compared to maintaining the state of the current office area.
West Dunbartonshire Council has secured a £500,000 grant to restore the Dumbarton Academy building.