United Airlines flight #UA125 was travelling from Athens, Greece to Newark in the US.
The Boeing 767-300 jet was about 150km west of Donegal when the crew reported an issue with the number 2 engine at around 2.20pm.
The crew did not declare an emergency until just minutes before they were due to land, when they the confirmed they had shut down the affected engine.
There were 199 passengers and a crew of 12 on board.
The flight entered a holding pattern for a time but shortly afterwards, the pilot told controllers they had shut down the affected engine and were formally declaring an emergency.