All flights at the airport were grounded for a period after the alert.
Passengers were held on the plane on the runway for up to 40 minutes while officers carried out safety checks.
Others saw police and fire crews on the runway who were waiting to meet the easyJet plane as it arrived from Poland.
Joel Smith tweeted: “Gatwick Airport stopped. Just landed but stuck on tarmac. Flight captain says ‘due to a security threat made towards aviation’. Emergency services currently checking aircraft.”
A bomb threat that turned out to be a hoax was made to the plane while it was still in the air, Sussex Police said. The flight landed safely 10 minutes later and “went to a remote area of the airport while emergency services attended”.
A police spokesman said: “It was swiftly established that the call did not relate to a genuine threat, everyone on board left the aircraft normally and passengers went on their way.
“We worked with Gatwick Airport management and with Air Traffic Control to ensure the incident was resolved quickly and safely and there was minimal impact on the normal routine of the airport.”
EasyJet said police boarded the flight because of a “safety-related issue”.
An easyJet spokeswoman said: “EasyJet can confirm that the flight EZY8512 arriving from Krakow on 7 December was met by the police upon arrival at London Gatwick as a result of safety-related issue.
“The flight was cleared by authorities and landed in line with standard procedures and passengers disembarked as per normal.
“We take very seriously any security threat to ensure the continued safety and security of our passenger and crew.”
Another passenger wrote: “It’s never good when your plane is welcomed by fire brigade and police climbing up the ladder,” and posted a photograph of four officers, two in helmets, preparing to board the plane.
Mr Smith later added: “Non-specific threat made to Polish police against easyJet and so was protocol to check aircraft.
“Final update: Pilot advised it was a hoax.”
No one from the airport was immediately available for comment.
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