Giving an idea of how many people were affected, the airport added: "5,000+ meals are being delivered to passengers.
"Power has been restored on all concourses," the Hartsfield-Jackson Atlanta International Airport said on its Twitter account, about 11 hours after first reporting an electrical disruption.
Giving an idea of how many people were affected, the airport added: "5,000+ meals are being delivered to passengers. Trains will be operational soon."
It did not indicate how long it might take to clear the backlog of flights but said it was offering affected passengers "free parking until 8:00 am", or for about eight hours after the lights came back on.
The Georgia Power company, in a statement, said "power had been restored for all essential airport activities including all concourses and flight operations."
It described the outage as "very rare" and said preliminary investigation suggested that a fire damaged cables and caused the power disruption.
"No personnel or passengers were in danger at any time," the company said.