He signed a deal until 2024.
Omonia officials sacked former Rangers defender Henning Berg as their manager a week ago and quickly identified Lennon to replace him.
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The Northern Irishman was keen to return to work 12 months after leaving Celtic.
He hopes Cyprus can broaden his coaching horizons after working in the United Kingdom until this point in his career.
After distinguished playing years with Crewe Alexandra, Leicester City and Celtic among others, he went on to manage Celtic twice, Bolton Wanderers and Hibs.
He helped the Edinburgh club gain promotion back to the Scottish Premiership in 2017 before returning to Parkhead for a second spell with his boyhood heroes.
His managerial achievements include five Scottish league titles, four Scottish Cups and a League Cup, plus Manager of the Year awards in 2012, 2013 and 2020.
He brought ten pieces of silverware to Celtic across his two spells in Glasgow’s east end.
Omonia are in the bottom half of the Cypriot First Division and badly need to improve.
They also wanted a manager who, in time, can help them perform better in Europe.
They were eliminated from the Champions League, Europa League and Europa Conference League earlier this season.
Lennon’s achievements with Celtic in the European environment – helping them reach the Champions League knockout phase – made him an attractive proposition in Nicosia.