The 42-year-old Lennon parted company with the Hoops today after four hugely successful years at the helm amid suggestions he was ready for a new challenge.
Republic of Ireland manager O'Neill headed for Aston Villa and then Sunderland after his own spell at Parkhead, and is confident his fellow Ulsterman would be a success in England.
He said: "Why shouldn't he be? He has got really good experience now. He has had the experience of managing what I believe is one of the best clubs in the world.
"He has taken that on and that will stand him in great stead for the rest of his career."
O'Neill learned of Lennon's departure shortly before he put his Republic players through their paces in Malahide on Thursday afternoon, but insisted he had no inside information as to his reasons.
He said: "I don't know the ins and outs. I only heard before we went to training there about an hour and a half ago about the news.
"Neil has done very well. Obviously, I know him particularly well because I signed him twice as a player, once to Leicester City and once to Celtic, and he did exceptionally well for me in both spells.
"I really don't know the reasons for it, but it's happened. He's had a very good time at Celtic, particularly the year where they did brilliantly in the Champions League.
"But again, I really don't know."
Former Bhoys striker Henrik Larsson, currently in charge of Swedish side Falkenbergs, was swiftly installed as the bookmakers' favourite to succeed Lennon, although his price eased as punters turned to sacked Manchester United manager David Moyes.
O'Neill said: "Larsson was just phenomenal - phenomenal - as a player. Just when you were in a tight spot in many a game, you just looked to him and he would pull you out of it, so he was really terrific as a player.
"He then went on to great things as well for short periods at Barcelona and at Manchester United to prove that he could score goals in any part of Europe, and again that was terrific.
"He's had a little time as well as a manager in his own country, and if you say they have stopped taking bets on it and that he is a very, very strong favourite, why not?
"He would be a great fit for Celtic again."
Larsson also received the backing of one-time team-mate Aiden McGeady, who is certain he would be welcomed with open arms by Celtic fans.
The Everton winger said: "That would go down well, I think, with the fans, very well. I was lucky enough to play alongside him and he is so highly thought of at Celtic.
"He's in every fan's greatest ever XI, an absolute legend, so if he was to get it, I think the fans would be pretty happy."
But as Celtic launched the search for a replacement, there was almost as much speculation over Lennon's next destination, and another former player believes the former Northern Ireland midfielder will already know where he is going.
Pat Bonner told talkSPORT: "I am sure he has something lined up. When you are winning things, in the Champions League, you are hot property.
"I would be shocked if he left without having a club."