An Ethiopian man born in 1983, the co-pilot has sought asylum due to fear of persecution in Ethiopia, police said at a news conference.
After locking himself in the cockpit, he asked to refuel at Geneva, landed the plane, climbed down from the cockpit window using a rope (available in the cockpit), and gave himself up to police.
He was unarmed and there was no risk at any time to crew or passengers, police said.
The situation inside the plane remained calm throughout.
The co-pilot himself alerted the authorities to the plane's hijacking, officials added - and passengers on the plane were unaware it had been hijacked.
The only possible offence the co-pilot could be charged with is that of hostage-taking, for which he could face up to 20 years of imprisonment, a Geneva prosecutor said at the news conference.
Flight 702 was scheduled to leave the Ethiopian capital, Addis Ababa, at 00:30 local time (21:30 GMT), and arrive in Rome at 04:40 local time.