Henrietta Yakubu, a spokesman for the aviation authority, said repair works were completed 24 hours ahead of schedule.
An Ethiopian Airlines flight was the first to land on Tuesday morning.
Flights had been diverted to Kaduna, 160 km (100 miles) from the capital, and some international carriers refused to operate the new route.
Those airlines are now taking bookings for flights later this week.
The Ethiopian Airlines crew was welcomed with champagne
The runway at the airport needed some serious attention
The runway at Nnamdi Azikiwe airport was supposed to be upgraded in 2002 - it was built in 1982 and was only meant to have a 20-year lifespan.
There have been celebrations that the repair project was completed ahead of time but the fact the capital was without a functioning airport for more than a month highlights the state of Nigeria's crumbling infrastructure, the BBC's Martin Patience says.