The pair, from Crawley in West Sussex – just a few miles from the airport – are being held on suspicion of disrupting an airport.
Many flights are still being delayed after three days of disruption, which began on Wednesday night.
Hundreds of flights were grounded over the three days, and more than 100,000 Christmas travellers were affected.
Sussex Police said the pair being held were arrested at about 10pm in Crawley town on suspicion of disrupting services of civil aviation aerodrome to endanger or likely to endanger safety of operations or persons.
“We continue to urge the public, passengers and the wider community around Gatwick to be vigilant and support us by contacting us immediately if they believe they have any information that can help us in bringing those responsible to justice,” Superintendent James Collis added.
“The arrests we have made are a result of our determination to keep the public safe from harm. Every line of enquiry will remain open to us until we are confident that we have mitigated further threats to the safety of passengers.”
He added that police are deploying tactics to “build resilience to detect and mitigate further incursions from drones”.
Cold and noisy: Sleeping under the stairs at Gatwick
A Gatwick Airport spokeswoman confirmed flights had resumed on Friday evening after being suspended for more than an hour when a drone was spotted at about 5.10pm.
Military measures in place meant it was safe to fly despite the “confirmed sighting”, the spokeswoman said.
Equipment deployed to stop further drone chaos is believed to be capable of jamming signals to the rogue devices as well as tracking them.
What are passengers’ rights after the drone chaos?
Find out what you can claim if your flight was cancelled or delayed
The airport faced a total shutdown on Thursday and part of Wednesday night when drones repeatedly violated its perimeter.
Some passengers described freezing conditions as they slept on benches or on the airport floor.
Conservative peer Lord Ashcroft offered a £10,000 reward for information that led to the arrest and charge of the drone operator.
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