An all-party inclusive agreement will see the Mountcharles man elected to the position.
It had been reported that Sinn Fein’s Jack Murray was to be the new chairman but this is not the case.
Nicholas Crossan from Buncrana has been selected as the vice chairman of the council.
All 37 councillors are currently meeting at County House in Lifford for the first meeting of the newly-formed council.
Cllr Ciaran Brogan of Fianna Fail said he was pleased with the selection of Cllr Campbell and said he hoped the make-up of the new council would be a fruitful one for the people of Donegal.