"One factor taken into account is a letter of regret from Mr Ambrose which has been sent to the Prime Minister and Mr Banks. They have both indicated acceptance of this statement."
The prime minister Mr Key welcomed the police decision not to lay charges.
"I also welcome Bradley Ambrose's letter of regret," said Mr Key.
"I note that the police statement today contains the comment that, while Mr Ambrose has been issued a warning, the police are clear that his actions were unlawful.
"As the complainant in this matter, my views were sought by the Crown Solicitor on whether I thought Mr Ambrose should be prosecuted.
"In light of Mr Ambrose's letter of regret, I indicated that I did not believe a prosecution was now necessary," said Mr Key.
"The decision announced by the police today, and Mr Ambrose's letter, allow all concerned to move on from the situation."
Mr Ambrose says he recorded the conversation inadvertently at the staged event to which media were invited to witness and report on Mr Key's endorsement of Mr Banks.
However, Mr Key laid a complaint, saying the conversation was private and Mr Ambrose's recording of it was illegal.
The tape, in which Mr Key made comments about NZ First's voters and discussed the future leadership of the Act Party, dominated media coverage in the final weeks of the election campaign.
It also provided a boost to NZ First leader Winston Peters, who leaked what he alleged were the contents of the conversation, to gain traction in the media.
Mr Key made his complaint to the police shortly after the incident but Mr Ambrose then went to the High Court asking for the conversation to be declared public. However Justice Helen Winkelmann was unable to make a judgment on the matter.
Attorney-general Chris Finlayson is seeking nearly $14,000 in court costs from Mr Ambrose over that High Court action in a matter that remains before the courts.
The contents of the tape cannot be published by APNZ after police reminded media outlets that it is illegal to disclose the contents of a private conversation that has been unlawfully recorded.
However, during the election campaign, Mr Peters said Mr Key and Mr Banks had undermined then-Act leader Don Brash, and that the PM had made derogatory comments about the pensioners who usually support New Zealand First.
Mr Key has apologised to older New Zealanders if they were offended by his comments.
"Older New Zealanders at some point pass away, and it's a statement of fact that Winston Peters' base has typically been represented by older New Zealanders," he said.
"But that was a private conversation. I would always phrase things in a better way if it was a public conversation. So if there was offence, yes, I would apologise for that."