Flights and terminal services were disrupted due to the outage which is reported to have happened just before 9am.
Only emergency lighting was available for around an hour with an airport spokesperson stating that the power was returning.
Check-in and security features were out of use during the power cut as passengers were left stranded at the airport and flights grounded.
It is not yet known the cause of the power cut or how long it will be until the power is fully restored.
An Edinburgh Airport spokesperson said: “We can confirm that power is now returning to the terminal and that flights have resumed.
“We’re working to allow passengers to continue their journeys in a safe and ordered manner and we thank passengers for their patience whilst we do this.
“As always, the safety of passengers and staff is our priority.
“We expect there to be further delays whilst we clear the backlog.”