Flights from/to Glasgow and Aberdeen are also affected from the fault which is believed to have risen overnight at the main control centre in Prestwick.
Edinburgh Airport says there currently has been no cancellations as a result of the glitch.
Passengers are being advised to contact their airline to find out the state of their flight regardless of whether they are heading in or out of Scotland.
Arrivals board at Edinburgh shows morning flights from Heathrow, Bristol and Gatwick are running up to 90 minutes behind schedule.
Also, departures from Edinburgh have been delayed by more than an hour.
Aberdeen Airport says a small number of delays were affecting some flights but it was hopeful they would be back to normal "as soon as possible".
Some passengers on social media expressed frustration at the announcements being made about the technical fault.
One passenger had claimed they were stuck on a plane at Glasgow as they waited to fly to Paris via Amsterdam.
Sky News UPDATE: Edinburgh Airport says there will be delays to all flights this morning due to "ongoing issue" with air traffic control in Scotland
