After a night-long operation, the aircraft was lifted at 6 am with the help of huge cranes. A 100-member expert team from Mumbai was at the spot to assist the operation.
Airport sources said the runway has been cleared and normal services would soon resume at the airport.
The runway had initially been closed for 10 hours in the aftermath of the mishap and was later partially opened for smaller aircraft.
The plane, with 137 passengers and six crew, veered off the runway at 3.55 am on Monday, breaking its nose-wheel. One person was hospitalised with fractures and six with minor injuries discharged after first aid.
Before total clearance of the 3,400m runway, two flights of Gulf Air and Etihad were diverted to Chennai and an Air Arabia flight to Coimbatore, the sources said. A Jet Airways flight from Doha was diverted to Thiruvananthapuram, they said.
Cochin International Airport Limited Managing Director V J Kurien had said that strong winds and heavy rains which lashed Kochi on Monday could have been the cause of the mishap.