The 42-year-old former Sunderland and Ipswich boss had been out of the game since January 2011 when he got the call from O'Neill, and he revealed the offer to work with his country once again was one he could not refuse.
Keane said: "I know people think I am a little bit crazy, but I would have been crazy to have turned it down, it was just too good an opportunity.
"There wasn't one bone in my body that said, 'No, this is not for me'. As soon as I met Martin and we discussed it, I thought, 'yes'. There was nothing to discuss. I just sad, 'Yes, let's go for it'."
Keane took his first managerial job at the Stadium of Light at the age of just 35 back in August 2006, and guided the Black Cats to promotion back to the Premier League in his first season.
He departed in December 2008 with the club languishing in the lower reaches of the table, and he spent a little more than 20 months at Ipswich before his reign was brought to an untimely conclusion.
However, the former Manchester United star is convinced he should have had more chances than he had to return to football before O'Neill brought him in from the cold.
He said: "I have had two opportunities to get back into football - one was working abroad, another was an international job - and it didn't quite fall into place, but there are certainly clubs in England I feel should have given me an opportunity.
"But a lot of coaches say that, so yes, it was frustrating, but also you need to be patient and wait for the right opportunity.
"I am just glad that someone like Martin O'Neill said, 'Listen, do you fancy coming and working with me?', and really with the Irish team, it seemed like such a good fit, I couldn't say no."
O'Neill revealed as he was unveiled on Saturday that there was no clause in his two-year contract that would allow him to leave for another job, and Keane is not even thinking along those lines.
He said: "We have signed a contract for the next couple of years, and that's the focus.
"It's always dangerous to sign any kind of contract thinking of some sort of get-out or what might happen further down the road. That's not in the mindset."
Keane is confident he can improve the players in the Ireland squad, and particularly the midfielders, although he was mystified by reports that he had told former international Ray Houghton that there are bigger talents in the current set-up than he was in his day.
He said: "I don't think I said that, no. I don't remember saying that. I don't know if Ray had a few pints in him.
"Maybe I said something along the lines of maybe there is more potential, and sometimes the players are the last to think that.
"Maybe there has been a mentality that when they play for Ireland or even at club level that sometimes they don't realise how good they are."