Dugan, a Carrollton construction company official, received 3,300 votes to 467 votes for Camp in the special election in the three-county district.
Dugan received 2,620 votes to 446 for Camp in Carroll County.
Douglas County residents voted 446 for Dugan to 102 for Camp. Paulding County voted 233 for Dugan to 57 for Camp.
Dugan will succeed Bill Hamrick after Gov. Nathan Deal appointed Hamrick to a Superior Court judgeship.
The Legislature is set to begin its 2013 session Monday.