"Leo has been an unbelievable leader for the organisation on and off the field. I think given that Jono is moving off to Clermont, it was the natural progression for Leo. He's got all that knowledge, he understands what's required at the very top level and I'm really looking forward to working with him," said O'Connor.
"You don't have to talk to people for too long to understand whether they'll be able to do it or not. Leo's demonstrated that he's certainly got the knowledge.
"When you sit down and have the conversation with him, the genuine excitement and student of the game that he is, you know he will thrive in the environment.
"He's certainly a leader and he's got vast rugby knowledge and experience. I wouldn't doubt that he'd be a very good head coach, but it's just about how the thing twists and turns, how long he wants to be in the game."
Cullen only recently returned to action after surgery and will be looking to add to his collection of three Heineken Cup winners' medals, and an Amlin Challenge Cup title, with Leinster in his final campaign.
He made his European rugby debut on October 17, 1998, in a Heineken Cup pool clash with Stade Francais Paris. In the last round of pool matches earlier this month, he made his 92nd appearance in Europe for Leinster and Leicester Tigers, and his 90th in the Heineken Cup.
As well as his four winners' medals, he also picked up a losing Heineken Cup medal with the Tigers in the 2007 final at Twickenham Stadium against London Wasps. His vast European experience, allied to 32 Irish caps, three as captain, make him an ideal candidate to take over from Gibbes.