A Med-View Airline flight with 82 passengers on board, including the Borno State governor Kashim Shettima, touched down at about 2:00 pm (1300 GMT).
Nigeria's military, which has a base at the airport, announced the re-opening of the facility last month.
The airport was shut in December 2013 after a daring assault by hundreds of militant fighters that saw them burn military aircraft on the tarmac and seize a cache of weapons.
Bankole said he was hopeful the Boko Haram insurgency would not affect operations.
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"Allah is the owner of security. We are all at the mercy of Allah. We pray for our brothers... That they should know that peace is the solution," he told reporters.
Boko Haram began life as a largely peaceful anti-corruption movement in Maiduguri in 2002, turning violent in 2009 after the death of its founder in custody.
The city has come under repeated attack, especially since the inauguration as president on May 29 of Muhammadu Buhari, who has vowed to crush the uprising.
In the last 18 months only military planes and emergency personnel have been allowed to use the airport.