The Egyptian airliner said negotiations had resulted in the release of all those on board Flight MS181 apart from the crew and four foreign passengers.
Video from Larnaca airport has shown people leaving the plane and boarding a bus.
It was taken over after a passenger said he was wearing an explosives belt.
Latest reports from Cyprus media suggest there is just one hijacker who was motivated by “personal reasons” and may be seeking asylum – although this has not been confirmed.
EgyptAir said the Airbus A320 was carrying 81 passengers from Alexandria to Cairo.
A senior Alexandria airport official said those on board the flight when it took off included 30 Egyptians, eight Americans, four Dutch, four Britons, two Belgians and one Italian.
Larnaca airport, on the south coast of Cyprus, has been closed and scheduled flights diverted elsewhere.
“The pilot said that a passenger told him he had an explosives vest and forced the plane to land in Larnaca,” the Egyptian civil aviation ministry said in a statement.
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