He will take up the post in June, following Mr Jeyes's departure to work with Cambridgeshire county council.
Stirling made its appointment over the head of the long-serving internal candidate, Margaret Doran, its head of schools.
It says Mr Cameron, who has been in the education directorate for more than 20 years, first in Fife and then in East Lothian, had "a strong track record in senior management with local authorities." Seen by some as a charismatic performer, Mr Cameron will take over one of the pioneering authorities in the integration of education and other services for young people.
Corrie McChord, leader of the council, said: "David Cameron has a considerable background as a teacher and manager in schools. He brings a wide experience of involvement in all sectors of education and of work with other services and agencies.
"He has a clear vision for how the very good services for children in Stirling can be further improved by working with parents, children and across all professions."