Gatwick chief operating officer Chris Woodroofe said the airport has scheduled almost 700 departures for today.
Mr Woodroofe, speaking to BBC Radio 4's Today programme, said: "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."
Mr 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 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."