Like City, Omonia came through two qualifying rounds and disposed of Greek giants AEK Athens in the previous round while City scraped through on penalties against Danish minnows FC Midtjylland.
Omonia have won the league championship in Cyprus 19 times, their last league title coming in 2003, and their last trophy was the Cypriot Cup in 2005.
They qualified for the UEFA Cup by finishing 3rd in the Cypriot First Division last season, and the country's football fans are on a high after Anorthosis Famagusta also beat Greek opposition in the form of Olympiacos to become the first Cypriot side to make it into the Champions League group stage.
Their key players are Clayton and Cafu, although the latter is not Brazil's World Cup-winning captain. Clayton is a journeyman Brazilian forward while Cafu is a Portuguese-born Cape Verde international that plays up front.
Omonia play in the GSP Stadium in Nicosia, which holds a healthy 23,000. Nicosia is the Cypriot capital and is situated in the centre of the island.
The first-round ties will take place on September 18 and October 2, with City at home for the first leg.