The £5m centre is expected to create more than 150 jobs over the next three years.
It will become the firm's UK hub for training apprentices for the maintenance and servicing of fighter jets.
The academy will include a hangar, training aircraft and workshops and will take on 60 apprentices a year.
Martin Blaze, director of aircraft maintenance and support at BAE Systems, said: "This academy gives us the opportunity to develop the individuals to the highest level of competence to ensure safe operations.
"We also anticipate that BAE Systems personnel from places such as Saudi Arabia and Oman will come to this facility to be trained to then return to work in their country, which will be a huge feather in the cap of all concerned."
Paul Litten, commercial director at Humberside Airport, said: "This prestigious development further underlines the importance of the airport to the region and will give a much needed boost to the growing requirement for aviation engineers."
A multi-million pound training academy is to be built by defence firm BAE Systems at Humberside Airport.