The UK's National Air Traffic Services (Nats) has blamed a software glitch at its centre at Swanwick in Hampshire.
The inquiry will look at Nats' handling of the episode and whether lessons were learned from previous failures.
UK Transport Secretary Patrick McLoughlin will then be questioned by British MPs about the incident.
The UK's Civil Aviation Authority (CAA) says it will appoint an independent chair to lead the inquiry, which will take evidence from experts on information technology and air traffic control.
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Other UK airports reported knock-on effects.
Heathrow Airport also cancelled about 40 flights on Saturday morning before normal services resumed.
The incident comes a year after a telephone failure at the Hampshire control room which also caused flights to be disrupted - one of a number of technical hitches to hit the partly-privatised Nats since the Swanwick centre opened in 2002.
The transport secretary said the system failure was "unacceptable" and asked for a full explanation from Nats about what went wrong.
But Nats chief executive Richard Deakin rejected the criticism.
He told BBC that Friday's issue was not "due to a lack of funding" - rather it was "one error, or limitation, in four million lines of code".
"Over the next five years we are spending around 575 million British Pounds on new systems. We have the funding that we need to deliver the service that we require," he added.