Flights in and out of the airport were suspended on Wednesday night, with the shutdown continuing throughout Thursday despite a brief reopening in the early hours.
At just before 6.30am on Friday, Gatwick said the runway was "currently available", with "limited number of aircraft" scheduled for departure and arrival.
The airport continued to urge passengers to check the status of their flights before travelling and warned that people could still face delays and cancellations.
According to flight tracking website Flightradar24, a plane landed at Gatwick from East Midlands Airport at 5.58am, while the first flight to depart left at 6.33am heading to Lapland.
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The reopening comes despite no confirmation from police that a drone has been brought down or that there have been any arrests.
On Thursday night, police revealed there had been more than 50 sightings of the drone in the 24 hours from 9pm on Wednesday, when the airport first closed.
Detective Chief Superintendent Jason Tingley, of Sussex Police, said at the time that shooting the drone down was being considered as an option after other strategies had failed.
Police were working on the assumption that the drone had been modified, with the "intent of causing disruption", and were looking through CCTV to identify the make and model, he said.
Mr Tingley added that they were following up a "number of persons of interest" in their investigations, with the military drafted in to offer additional support to officers.
According to reports, one line of inquiry was that a lone wolf eco-warrior was behind the incident.
Chris Woodroofe, Gatwick's chief operating officer, said 120,000 passengers' flights had been disrupted.
He refused to comment on the possibility of the airport awarding compensation to passengers who had been affected by the chaos.
He added: "The issue from my perspective is that this has been a criminal act purposefully undertaken in order to cause this disruption and I very much hope we bring the perpetrator to justice."
The incident led to calls for more action to tackle illegal drone use.
The runway was closed almost constantly after two drones were spotted being flown inside Gatwick's perimeter.
It was reopened at 3am on Thursday but shut again 45 minutes later after the drones re-emerged.
Transport Secretary Chris Grayling said there was no known motive for the pilot of the "commercial" drone.
Passengers faced severe disruption as flights were unable to leave the tarmac at Gatwick, while many inbound flights were diverted to alternative airports as far away as Amsterdam and Paris.