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Mr Cull wrote to the two men offering an apology for any "distress or harm" caused, and the council agreed to contribute $29,000 towards the pair's legal costs, a copy of the settlement agreement said.
The pair began defamation proceedings against Mr Cull in April, after the mayor questioned the performance of the union's former board in a Radio New Zealand interview on March 15.
Messrs Graham and Mains - the board's chairman and deputy chairman until earlier this year - said in a joint statement yesterday the matter had been "settled amicably" after a "genuine apology" by Mr Cull.
A copy of his September 24 letter to the pair was released by them yesterday.
It showed Mr Cull apologised if his strongly-worded comments had been interpreted as "personally critical of either of you or any individual member" of the board.
"I regret that I did not make it clear that my comments were not directed at any individuals, and apologise to you for any personal inference that has been taken from my comments, and for any distress or harm this may have caused you," he wrote.
Mr Cull declined to comment yesterday, but a copy of the settlement agreement and other documents were released to the Otago Daily Times following an official information request.
The settlement showed the parties acknowledged Mr Cull did not admit liability, but had decided to settle the dispute.
Councillors approved the $29,000 payment in the non-public part of last week's Dunedin City Council meeting, with Crs Lee Vandervis and Fliss Butcher voting against.
The "pragmatic approach" came after legal advice and was to "minimise potential risk and cost to the council", the meeting's minutes showed.
The ODT first reported in April the threat of legal action against Mr Cull.
Court documents later showed Messrs Graham and Mains were each seeking $500,000 in general damages, unspecified "special damages", plus interest and costs, for alleged defamation.
Mr Cull's comments came after the council agreed to wipe $480,000 owed to it and Dunedin Venues Management Ltd by the ORFU as part of a wider bail-out that saved the union from liquidation.
Messrs Graham and Mains, in their statement, said they were pleased the outcome acknowledged they were recent ORFU appointments, had inherited major issues facing the union and had "done their utmost to remedy a difficult situation".
Mr Cull's letter to them said he was aware both had received "significant adverse comment" following his comments.
That was "regrettable" and not intended, Mr Cull wrote.
He acknowledged the contributions made by both men - in time and money - to rescue the union from liquidation and help repay small creditors.
"I do not question the honesty or sincerity of either of you in this process."
Mr Cull hoped both sides could now "put this behind us" - a sentiment echoed by Messrs Mains and Graham.