The plane's second-in-command, who was not carrying a weapon, reportedly took control of the plane when the pilot left the cockpit to use the toilet.
After landing, he left the aircraft through a cockpit window using a rope, without harming passengers or crew.
Police spokesman Pierre Grangean said: "Just after landing, the co-pilot came out of the cockpit and ran to the police and said, 'I'm the hijacker'. He said he is not safe in his own country and wants asylum."
As passengers left the plane, which was parked near the end of the runway, they were checked by police.
Opposition groups and human rights campaigners in Ethiopia accuse the government of stifling dissent and torturing political detainees.
However, it is rare for government officials and employees - Ethiopian Airlines is run by the state - to seek asylum. The last senior official to do so fled to the US in 2009.
Flight ET702 had left the Ethiopian capital Addis Ababa on Sunday evening and was bound for Rome. The plane was hijacked while over northern Italy.
There were 193 passengers on board the Boeing aircraft, including 140 Italians.