The 30-year-old tried to pass through a staff search area in the South Terminal just before 2am yesterday carrying a knife in each hand.
The area was secured and he was challenged by armed police officers who used a Taser to detain him.
He was arrested on suspicion of possessing offensive weapons and making threats to kill, and was detained under the Mental Health Act.
Police said it was not being treated as terrorist-related and that the man, from Crawley, West Sussex, was not a travelling passenger.
The terminal’s baggage reclaim area was temporarily evacuated as a precaution.
Supt Justin Burtenshaw, from Sussex Police, told the BBC: “This incident was dealt with swiftly and no members of the public or police were harmed.”
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