O'Neill joked that he could ask Sir Alex Ferguson for advice on how to handle Keane if he causes any trouble, but O'Neill is expecting nothing of the sort.
The 61-year-old incoming Republic boss, who was formally unveiled at the Gibson Hotel in Dublin on Saturday afternoon, sprang a major surprise when he approached the former Manchester United skipper to become his number two.
Keane, 42, famously returned from the Republic camp just days before the 2002 World Cup finals in the Far East after condemning the nation's preparations for the tournament and, in the process, falling out with then boss Mick McCarthy.
He recently found himself on the wrong end of a Ferguson broadside when the Scot's autobiography was published, but O'Neill insists he has no qualms about employing an assistant who could hardly enjoy a higher profile.
O'Neill said: "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.
"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, he 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."
O'Neill added with a smile: "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."