Heathrow said it was causing "intermittent" problems, but that passengers were still able to check-in, "although the process may take slightly longer than usual".
Amadeus, the Spanish travel technology that provides the software, confirmed a "network issue" had been causing disruption.
In a statement at shortly before 2.30pm, it said: "Amadeus can confirm that our systems are recovered and are now functioning normally.
"During the morning, we experienced a network issue that caused disruption to some of our systems. As a result of the incident, customers experienced disruption to certain services.
"Our technical teams took immediate action to identify the cause of the issue and mitigate against the impact on customers. Amadeus regrets any inconvenience caused to customers."
Frankfurt airport operator Fraport said that Germany's largest carrier, Lufthansa, and partner airlines had been hit by a problem for around 30 minutes that prevented bags being checked in, but said the issue had been resolved.
A spokesman for Groupe ADP, which operates more than a dozen airports in the greater Paris region, confirmed airlines using the Amadeus system had been affected at the French capital's Charles de Gaulle airport.
"This was a worldwide failure (of the Amadeus system). We were no worse affected than other airports. It only lasted a few minutes," the spokesman said. He said national carrier Air France was among the airlines that used Amadeus.
In Washington, a spokesman for the Metropolitan Washington Airports Authority said Southwest Airlines reported a computer issue causing a few minor delays at Reagan National Airport of up to 16 minutes but there were no other issues at present.
Passengers whose flights are delayed as a result of the IT glitch should be entitled to compensation if it is not classed as an "extraordinary circumstance".
