Twenty-eight flights were cancelled and 26 diverted to other airports after the problems began at about 17:00 BST.
The airport said it had experienced a problem in its control tower.
Flights are still delayed by an hour or more, with cancellations expected throughout the evening, Gatwick said.
The effects were felt at airports across Europe, with many inbound flights to Gatwick cancelled and others expected to be delayed by about three hours.
Passengers due to travel to or from the airport have been advised to check for updates with their airline.
EasyJet said Gatwick was operating at a “reduced rate” and apologised for the disruption, which it said was “outside of our control”.
A spokesman said the airport aimed to return to a full schedule on Thursday without delays, adding: “The ambition is it should run as usual.”
Colin Franks, who was due to board an EasyJet flight to Palma, Spain, at 18:00 said he was “trapped between the boarding gate and the air bridge”.
He said the plane’s pilot had spoken to passengers, adding: “He said they had been given a provisional [take off] time of 10pm.
“At the moment, everybody is talking to one another and it’s quite cheery. There are a lot of children here.”