The £60 million scheme will see the new schools built next to the existing buildings.
Once pupils have moved into the new facilities, the old buildings will be demolished to make way for playing fields, social spaces and car parking.
The new school at Oban will house 1,300 pupils and is expected to be completed in spring 2018.
At Campbeltown, the three-storey facility will accommodate 500 pupils and contain associated new 3G sports pitch, music pavilion and enlarged car parking as well as a new dedicated pupil drop off area.
It is also expected to be finished by spring 2018.
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Both of the schools are being delivered by the council in partnership with hub North Scotland and the Scottish Futures Trust through the Scottish Government's Schools for the Future Programme.
Douglas Hendry, the council's Executive Director for Customer Services, said: "Obviously we are very pleased to have reached this key stage in our new schools programme. The initiative is based on building high quality schools which will best serve our communities, delivering the Curriculum for Excellence and providing facilities for community use.
"The council is committed to building new, modern schools which will ensure a positive learning environment for our pupils.
"We are delighted to be moving into the construction phase, which will see the new secondary schools in Campbeltown and Oban completed by the spring of 2018."
Angus Macfarlane, chief executive of hub North Scotland, added: "Reaching financial close on both projects is a vital milestone in that it paves the way for construction on both to begin in earnest; I'm sure it will be warmly welcomed by all key stakeholders across the Oban and Campbeltown developments.
"hub North Scotland is delighted to have been appointed development partner for both projects and we look forward to working with Argyll and Bute Council as well as other project partners to deliver two first-class educational facilities."
(LM)
