In unofficial results, the four-term former city councilman beat out Val Applewhite - who's served on the city council since 2007.
Roberton had 11,529 votes - or 50.49 percent - to Applewhite's 11,271 - or 49.36 - meaning Applewhite cannot ask for a recount because the difference is greater than 1 percent if the results hold up.
The two were the top vote getters in October's five-candidate primary. Roberson replaces Mayor Tony Chavonne, who chose not to seek a fifth term.
"It couldn't be much more of a squeaker," said Robertson. "We had a great ground team, a great group of volunteers. We were just fortunate to land on top."
Robertson will be sworn in next month.