The former Northern Ireland international was unveiled in his new role at the Gibson Hotel in Dublin following the announcement that he and ex-Manchester United captain Roy Keane have penned a two-year deal with the FAI.
They will be in charge of preparing the Irish squad for the Euro 2016 qualifying campaign, which starts in September 2014.
Kilrea man O'Neill told the press that he had no qualms about approaching the former Man United skipper, who was absent on Saturday.
"I am absolutely delighted he is on board. He is an iconic figure, a great, great player, one of the best players to have played in the Premier League since its inception, a great, great player, so I haven't a problem with that there," the 61-year-old said.
"He went into management - I see Sir Alex Ferguson's points there that he said that perhaps Roy might have gone into management too soon. I don't really know that.
"All I do know is that from working with him over the last couple of years doing some television work on the Champions League games, I have found him very, very engaging.
"I have found his thirst for knowledge amazing. I see him at football matches when there's no need for him to be at games. He loves football."
I think like all of us in the game, (Roy) has points to prove. I know how brilliant he was and I know how sometimes how polarised opinions can be with Roy, but I don't have a problem with that.
Republic of Ireland manager Martin O'Neill
He added: "If you are asking about overshadowing, one of the greatest managers in the game finally decided that Roy was no longer wanted because he (Ferguson) felt he was going to be overshadowed.
"If he decides on the same thing, I might call Alex Ferguson up and see how he dealt with it.
"But all told, I think he will be great. I think he will be great for me for a start - I would like that - but more importantly, I think he will be brilliant for the Republic of Ireland."
The Republic boss revealed it took little time for Keane to make up his mind when the idea was raised.
He said: "I did mention to him about the possibility of working with me here, and it took him about four and a half seconds. He was absolutely delighted with it."
O'Neill admitted he had thought long and hard about making the move from club management on to the international stage and the differences between the two before committing himself.
In announcing the former Wycombe, Norwich, Leicester, Celtic, Aston Villa and Sunderland manager's appointment on Tuesday, Football Association of Ireland chief executive John Delaney revealed that he had turned down offers from Barclays Premier League clubs to take over the Ireland team.
O'Neill had been out of work since he was axed from his role with the Black Cats at the end of March - to make way for Paolo Di Canio's brief stint at the Stadium of Light.
The Republic team are due to meet in Portmarnock on Monday evening to begin training the following day ahead of the friendlies against Latvia and Poland, although the longer-term focus is qualification for Euro 2016.
O'Neill stated: "John has told me that it's my remit to get the team to France.
"My contract lasts for the duration of the time that the Republic are in the Euros, and that is my driving ambition."