After the final count of special votes, Mr Scott was 39 votes ahead of Southland farmer Geoffrey Young, and former mayor Gary Tong was six votes behind Mr Young.
Mr Scott said he was delighted with the result.
"I’ve just been trying to let everyone know that my iPhone is getting a workout.
"I need to get my battery charged up.
"I’m just unravelling all the nerves now. That’s turning into great excitement."
Following the announcement, fellow candidates Mr Tong and Mr Young called Mr Scott to congratulate him on the win.
"We all sort of really shared our thoughts on each other’s campaigns and how we all ran strong campaigns, and we’ve all wished each other all the best.
"There were no dirty politics in our campaigns or anything and we all got on really well throughout the campaign time," he said.
Mr Scott said he now had a few days to wrap his head around the results before he started talking to his team and working on the plan ahead.
"I want it so that we’re working with all the elected members and doing it that way.
"There’ll be plenty of time to do that and we’ll get there."
He congratulated fellow mayors-elect throughout the region, including 23-year-old Gore mayor-elect Ben Bell, who is now New Zealand’s youngest mayor, and said he was looking forward to working with them.
Mr Tong said he was proud of Mr Scott’s campaign.
"He’ll go ahead with leaps and bounds."
Mr Young wished Mr Scott well for his term.
"Naturally, I’m quite disappointed.
"I believe that I had some fresh ideas there to change the council — and hopefully the staff — a little to a more customer focus, but that’s the way things go.
"Rob’s a nice chap. I’ve certainly got nothing against him. He ran a very good campaign."
Otago Regional Council Dunstan constituency candidate Michael Laws said he was growing increasingly frustrated at the delay in releasing a result for the final seat on the council.
Mr Laws is leading with 9275 votes, while Tony Lepper is 29 votes behind with 9246.
The duo have been told a result was not expected to be announced until early next week.
The battle for the final two places on the Invercargill City Council is also still to be confirmed.
The race is close between incumbent Peter Kett (6295), Barry Stewart (6205) and Graham Lewis (6192).
By: Ben Tomsett