Local police say they recognized him in security footage as one of many people who sleep rough near the airport.
The door of the Loomis cash management company in terminal 2F had been left unlocked and the man, in his fifties, walked back out with two bags of cash.
He is now being sought by police.
At about 17:30 (16:30 GMT) last Friday, an alarm sounded at the cash management company's offices.
