Martin could not be reached for comment Tuesday night, but Smith confirmed he called Martin to congratulate him on his victory.
Martin received 10,310 votes to Smith's 6,537 in unofficial returns.
He will serve the last two years of a term won by Marty Haynes in 2014. Haynes vacated the seat in September after his election as the county's assessor of property.
Martin, who still has two years left as the District 3 school board representative, will leave the post open to appointment by the County Commission.