More than nine million passengers a year pass through the airport, which offers several direct flights to the United States and is trying to attract more.
The responsibility for security operations will now fall to the terminal manager in charge of day-to-day airport running.
The move was criticised by aviation security experts.
Norman Shanks, former head of BAA security, said: "This seems odd. The two jobs of security manager and terminal manager go hand in hand, but usually you would have different heads.
"There will need to be safeguards to ensure there is no compromise as a result."
Airport managing director Gordon Dewar said: "The safety and security of our passengers and staff is our foremost priority and is not compromised under any circumstances."