The airport said in a statement that "military measures" in place at Britain's second-busiest airport made it safe to resume flight operations.
It said take-offs and landings had been suspended earlier on Friday - for roughly 80 minutes - as a precautionary measure while an investigation was under way.
An airport spokeswoman said there had been a confirmed sighting of a drone.
Flights at Gatwick, which serves over 43 million passengers a year, had been shut down all of Thursday and for several hours on Wednesday evening due to drone sightings.
The shutdowns have caused chaos over the holiday period. Britain deployed unidentified military technology to guard the airport against what transport minister Chris Grayling said were thought to be several drones.
"This kind of incident is unprecedented anywhere in the world," he said.
Drones spotted flying near Britain's Gatwick Airport have forced the closure of the runway, causing flight chaos for 10,000 passengers. Source: Press Association
The motivation of the drone operator, or operators, was unclear. Police said there was nothing to suggest the crippling of one of Europe's busiest airports was a terrorist attack.
Gatwick's drone nightmare is thought to be the most disruptive yet at a major airport and indicates a new vulnerability that will be scrutinised by security forces and airport operators across the world. The army and police snipers were called in to hunt down the drones, thought to be industrial-style craft, which flew near the airport every time authorities tried to reopen it on Thursday.
The perpetrator has not yet been detained but the police said they had a number of possible suspects. No group has claimed responsibility publicly and police said there was no evidence another state was involved. Sussex Police assistant chief constable Steve Barry said they were keeping an open mind about who was responsible.
"In terms of the motivation, there's a whole spectrum of possibilities, from the really high-end criminal behaviour that we've seen, all the way down to potentially, just individuals trying to be malicious, trying to disrupt the airport," he said. The defence ministry refused to comment on what technology was deployed, but drone experts said airports needed to deploy specialist radar reinforced by thermal imaging technology to detect such unmanned flying vehicles.
Other ways to tackle them is typically by frequency jamming that can disable or disrupt control signals and the GPS signals that allow the drones to navigate. The drone sightings caused misery for travellers, many sleeping on the airport floor as they searched for alternative routes to holidays and Christmas family gatherings.
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