Lennon had been linked with recent vacancies at Sunderland and Leyton Orient but was sold on the move abroad after speaking with club bosses and immediately set his sights on lifting a trophy to add to his stacked collection from his time in charge of Celtic.
"I got a phone call from an agent at the weekend saying that Omonia would be interested in taking on my services,” he told talkSPORT.
"I did a bit of research on it, spoke to representatives of the club, the president and had a look at some of the recent games. I have to say I was quite impressed by the standard and attitude of the players.
"They are the current champions but haven't had a great season this year but are still in the cup competition which we obviously want to try and progress in.
"That's the target now, finish the season well and try and win a trophy."
The Northern Irishman was keen to return to work 12 months after leaving Celtic and hopes Cyprus can broaden his coaching horizons having spent all of his playing and coaching career to date in the United Kingdom.
He added: "You always have reservations about any of these things but I always fancied the opportunity to work abroad. I think it will be a nice climate change but that is not the be-all and end-all. I think more than anything it is a nice challenge and one that really appeals to me.
"It's a big club. I think it is quite a competitive league and at the end of it if you are successful there is the opportunity to take the club into Europe again.
"They've got a chance of winning trophies but it is the overall being back in the game and new challenge and culture to take on and see where it takes me.”
Lennon is reportedly targeting Mark Fotheringham as his assistant, the 38-year-old former Celtic youngster having experienced Cypriot football in a season spent at Anorthosis Famagusta during his playing career.
Reflecting on the acrimonious departure from Celtic last season in the midst of the failed 10-in-a-row bid, Lennon added: "I had a good time at Celtic. It didn't end well but I've been at Hibs and Bolton and done over 500 games.
"I sort of spent a lot of time in Scotland and wanted a new challenge and Omonia are going to give me this new challenge.
"It is very exciting, it is going to be different and take a little bit of adaption but having more and more looked at it and researched it, it ticked a lot of boxes for me.
"There is always the opportunity to come back again anyway, but for the short-term and the next sort of year or so my full focus is going to be on Omonia."