The resignation comes amid calls for him to step down after documents showed Cr Skelt was the subject of a sexual harassment complaint from an 18-year-old female staff member before his departure as manager of ILT Stadium Southland last month.
The council received Mr Skelt’s resignation on Thursday night, a statement said.
Cr Ria Bond was happy she would not need to resign after making a promise that she would quit if Mr Skelt returned to council.
"I think Nigel resigning was the only move that he could do. He lost all of his credibility for his role.
"I am absolutely pleased that he used his common sense and had the graciousness to do the right thing.
"That means I don’t have to resign because I have a lot work to do on the council to get projects over the line."
She believed now was the time to move on.
"It means that we can continue to stay focused, that we’re not being distracted by Nigel and heinous behaviour ... and then the councillors can get on with the job."
Cr Trish Boyle believed his resignation would help council to "move together forward", while Cr Darren Ludlow thought it was the only outcome available.
"It was inevitable. Even though what he’s alleged to be involved wasn’t a council thing, that has reflected poorly on us. Would have been difficult for him to carry on."
Deputy mayor Tom Campbell agreed.
"I think he’s made the correct decision. I don’t have anything more to say than that.
"No-one on council could have required him to resign from his role. He was democratically elected and had the right to stay.
"However, ... he needed to think about whether he still had the trust and confidence of the electorate.
"So he has decided to resign, and I think that was a great choice."
Invercargill Mayor Nobby Clark said Mr Skelt had spoken to him about his decision.
"I respect the decision he’s made — it could not have been an easy decision and just hope things go well for his family moving forward."
Council chief executive Michael Day said a by-election to fill his position would be announced soon.
It was expected it would cost the council about $120,000.
Mr Skelt’s resignation followed a complaint which included an allegation he asked the stadium staff member if she would be keen to do jelly wrestling naked.
Mayor Clark, who is also a stadium trustee, was informed of the incidents in a resignation letter in February, and worked to resolve the complaint by issuing a "serious warning" to Cr Skelt, directing him to get psychological counselling and closely monitoring his behaviour.
He also offered the teenager $3000 to cover lost income, counselling for the trauma and the option of working somewhere else at the stadium or at ILT.
Mr Skelt was the highest polling councillor at last year’s elections and was also leading one of the biggest council projects — Project 1225 — which will involve the construction of a new Southland museum and art gallery by December 2025.
Mr Clark said conversations about his substitute in the project were being held yesterday and an announcement was expected by early next week.
