Three attackers are reported to have opened fire at an entrance to the terminal building on Tuesday night and blew themselves up after police opened fire on them.
Turkish Prime Minister Binali Yildirim said the early evidence suggested that the so-called Islamic State was behind the attack. There was no immediate claim of responsibility.
The "vast majority" of victims were Turkish nationals but foreigners were also among the casualties, a Turkish official said.
The BBC’s Mark Lowen said Tuesday's attack looked like a major co-ordinated assault with Ataturk airport long seen as a vulnerable target with X-ray scanners at the entrance to the terminal but security checks for cars are limited.
Witnesses described deadly carnage and crowds in panic as the attackers struck one of the world's busiest airports.
It is the latest in a string of attacks in Turkey's biggest city this year. Turkey's largest airport is a major transport hub for international travellers, and the attack came at the height of the holiday season.
Turkey’s tourism industry is already in deep trouble after a series of attacks have left foreign tourists afraid of visiting the country.