Britain's National Air Traffic Service (NATS) said the glitch, which hit major airports including London's Heathrow, was caused by a faulty switch between its night-time and daytime operating systems at its control centre in Swanwick, southern England.
The error caused delays and cancellations for 11 hours at airports from Dublin to Glasgow, before NATS finally announced that the problem had been fixed.
"Operations are returning to normal," a spokesman for the agency, which is part-owned by the government and a group of airlines, said at 1930 GMT.
"We sincerely regret inconvenience to our airline customers and their passengers."
He added that the agency's communications system, used to contact air traffic control agencies across Europe, was "very complex" and the biggest of its kind on the continent.
Heathrow, one of the world's busiest airports, was the worst-hit by the glitch, suffering 228 cancellations -- 15 percent of the day's flights.
Long queues snaked through airports as frustrated passengers lined up to rebook their flights, with some complaining that they had to wait up to five hours to speak to airline representatives.
NATS said it handled approximately 300 fewer flights than normal, operating at around 88 percent of capacity.
But Eurocontrol, the European organisation for air navigation safety, said around 1,300 flights had been "severely delayed".
Many passengers took to Twitter to vent their frustration, with British Paralympic sailor Helena Lucas posting on her page: "Lots of angry people at Heathrow! Customer services is crowded with unhappy people!"
Irish budget airline Ryanair, which had 100 flights affected by the glitch, called for Britain's Civil Aviation Authority to take action to prevent a repeat of the problem.
"While we acknowledge problems can occur, where is the contingency? It's simply not good enough and the CAA needs to act now," the airline said.