Britain’s second-biggest airport received its first arrival just before 6am GMT on Friday after flights were halted just after 9pm on Wednesday.
The decision to re-open the hub came despite police and specially-drafted armed forces failing to find the drones or their operator, whose identity and motives remain unknown.
Passengers travelling today have been advised to check before they set off.
Gatwick’s chief operating officer, Chris Woodroofe, said the hub has scheduled almost 700 departures so far.
Woodroofe told BBC Radio 4’s Today programme: “Our advice to our passengers is to check with their airline on each of those flights that they’re intending to get, to establish whether it’s one of the flights that’s being operated or one of the flights that’s being cancelled, before they come to the airport.
“I’d just like to apologise to all of those affected over the last 36 hours – 120,000 passengers who were due to fly to their destinations or arrive into Gatwick who have not travelled.”
Woodroofe was pressed on why the airport had decided to reschedule flights while the drone had not been found, he said: “We have been working overnight with the police, with a number of Government agencies and with the military to put in place additional mitigating measures which have enabled me to reopen our airport.”
Asked if the “mitigating measures” meant the drone would be shot down, he said: “You’ll appreciate that there are certain things I can’t talk about in detail.”
According to Flightradar24, a plane from East Midlands Airport landed at Gatwick at 5.58am.
In an update on its website, easyJet, Gatwick’s biggest operator by passenger numbers, said: “Gatwick airport have confirmed that the runway is now open. We do expect that the number of departures and landings will be restricted to begin with, which means that we are likely to experience more disruption to the flying programme.
“We would like to request our passengers to continue to check the status of their flight on the easyJet Flight Tracker.”
In response to a customer on Twitter, British Airways said: “We’ve received confirmation approx 30 minutes ago from London Gatwick, advising the airport is back open and the majority of flights operating as scheduled”.
Police earlier requested help from the armed forces to help tackle the threat posed by the drones, described by officials as “industrial” and “commercial”.
Sussex Police, the local force, has yet to comment on its investigation to hunt down the operator of the drones.
But its assistant chief constable, Steve Barry, said officers now have “a number of options” around Gatwick’s perimeter to help prevent further disruption.
Compensation: What rights do passengers have?
According to consumer groups, passengers aren’t automatically eligible for compensation from airlines, as the situation at Gatwick this week is out of their control.
Consumer charity Citizens Advice said many travel insurance policies could provide compensation and reimburse expenses, however, but said passengers must remember to keep receipts.
Often policies require delays to last 12 hours or more, which would still be the case for thousands affected by this week’s chaos.
There may be an excess deducted from any successful claims, and cheaper policies may not include cover for delays or cancellations.
And Alex Neill, of Which?, said those affected should not have needed to cancel tickets, as operators should have provided alternative options or accommodation.
He said: “Whilst these extraordinary circumstances unfortunately mean you are not entitled to compensation, you may still be entitled to meals, refreshments, hotel accommodation or transfers.”
The government’s transport secretary, Chris Grayling, temporarily lifted night flight restrictions at other UK airports to ease congestion.
Grayling said those responsible for the drone incursions should face prison.
And he confirmed on Friday that “military capability” had been employed to combat the threat.
Pressed on whether that meant “lasers, drone catching nets or radio wave fences”, he said: “There are new technologies that are now available, some purely in the military arena, some beginning to appear on the commercial market that are able to take action against drones.
“There isn’t a single off the shelf commercial solution that does the job and so what’s happened is a variety of things have been done to create a sense, create that degree of confidence that Gatwick is now safe to fly in and out of.”
Grayling told BBC Radio 4’s Today programme it was an “unprecedented” situation and rejected the idea that police could simply “shoot down” the drone.
Gatwick sees over 40 million travellers a year and is second only to London Heathrow in terms of overall passenger numbers.
Drones: An increasing threat to commercial jets
What is the law around flying drones?
Earlier this year, new laws came into force which ban all drones from flying above 400ft and within 1km (0.6 miles) of airport boundaries.
Drone users who flout the height and airport boundary restrictions could face an unlimited fine, up to five years in prison, or both.
Research funded by the Department for Transport (DfT) found that a drone weighing 400g could smash a helicopter windscreen, and one weighing 2kg could critically damage an airliner’s windscreen.
Have there been any incidents at airports in the past?
According to the British Airline Pilots Association (Balpa), there were already 117 near misses between manned aircraft and drones up until November this year, compared to 93 for the whole of 2017.
This is not the first time an incident involving drones has been reported at London Gatwick.
In October, it was reported that a drone “put 130 lives at risk” after nearly hitting an aircraft approaching the airport over the summer.
According to the UK Airprox Board, the flying gadget passed directly over the right wing of the Airbus A319 as it was preparing to land at the West Sussex airport in July.
Also in October, a drone collided with a commercial aircraft as it was approaching to land in Canada.
There were six passengers and two crew on the aircraft and the drone connected with its wing, but fortunately it suffered only minor damage, allowing it to land safely at Jean Lesage International Airport in Quebec City.