He warned media against broadcasting the recording - which is still available online - and said the investigation sent a message that "the recording and distribution of conversations that are considered private is likely to lead to prosecution in the future".
Mr Burgess said investigators believed the recording was at least reckless but more likely deliberate.
In his letter, Ambrose says he had no intention of recording the conversation and he regretted passing on the recording to the Herald on Sunday.
Speaking in South Korea yesterday, Mr Key confirmed a deal was struck.
"Yes, I could have refused to accept the letter from Mr Ambrose and that may or may not have seen the matter taken through the courts, but I don't think much more would have been achieved from there.
"At the end of the day, his actions have been deemed unlawful."
While Ambrose's lawyer, Ron Mansfield, downplayed suggestions of a deal, he conceded he "had an expectation that the letter would be taken into account and that it would be considered favourably".
He dismissed the police claim that Ambrose's actions were unlawful.
"If they had a strong case they would proceed. I don't believe they thought they had any reasonable prospect of succeeding if they went to trial."
Labour Party leader David Shearer said Mr Key's complaint and the subsequent investigation, which occupied three officers part-time, was "a complete waste of time".
"Four months later, Mr Ambrose comes out with exactly the same statement as he did four months ago and it's enough to drop the case."
Though the letter was written eight days ago, "police decide not to pursue the charges three days after John Key goes overseas", Mr Shearer said. "It's all too convenient, it seems to me."
New Zealand First leader Winston Peters said the timing of the police announcement suggested an improper degree of co-operation.
"It invites the question as to whether or not there is a parallel discussion wrongfully going on between the government of the day and law enforcement officers."
Mr Peters said the cafe meeting "was a political stunt against the democratic interest of the country".
"It came horribly unstuck; he should have the guts to say so."
Ambrose's letter
March 18
The Right Honourable Prime Minister Mr John Key and the Honourable Mr John Banks
Dear Sirs,
As you are aware I attended your media meeting at the Urban Cafe, Newmarket. I was paid a small fixed fee to film the event for the Herald Online News Webb Page (sic). I was working alone on this occasion.
My camera radio microphone was left on your cafe table. It had been placed there by me in a rush to pick up audio while you were speaking to the media. I had not expected this and was not prepared for it.
I was having difficulty getting good footage due to the media scrum around you. So I moved off and away from the table area to try and get some workable footage from a different vantage point. In doing so I left the microphone on the table. My primary concern was to get film footage. When I later realised that I had left the microphone behind I returned to uplift it. I spoke to your staff who acknowledged they had taken possession of it, that it would not be returned and would be referred to the police. I did not realise at that time what the concern was or why. I had no intention of secretly recording any conversation.
Later that day when the existence of the recording became public I was requested to pass on what I had recorded. I accept that I did so without thinking properly about the effect this would have. I regret this decision.
As stated, I do regret passing this audio on to the Herald on Sunday due to the effects that this had had on those involved, including yourself. Contrary to what has been said by some people, this was not intentional, nor was it a "News of the World tactic". There was no money offered for the recording by the Herald on Sunday nor did they or any other outlet pay for it.
This whole event has been blown out of proportion by a number of people and I would like to put it behind me.
I just want to get back to work and not be known as someone alleged to have dubious ethics. This has been hard on me and my family.
I trust that you are prepared to accept and appreciate my regret for how this matter has unfolded and escalated for us all. lf I knew then what I know now, I would have deleted the tape at the first opportunity and not provided it to any other third party. I have become much wiser and more protective of my reputation as a result of this event and what has transpired.
Accordingly, I trust that you find this letter as a genuine statement of regret and that you may be understanding of my position and the sincere sentiments I have expressed.
Yours faithfully, Bradley Ambrose
