The attackers began spraying bullets at the international terminal entrance before blowing themselves up at around 10:00 p.m. (1900 GMT) Tuesday, Turkish authorities said.
It is the deadliest of four attacks to rock Turkey's biggest city this year, with two others blamed on ISIS and another claimed by a militant Kurdish group.
Though there was no immediate claim of responsibility for Tuesday's carnage, "the evidence points to Daesh", Prime Minister Binali Yildirim told journalists at the scene, using another name for the jihadists.
He said the dead included foreigners, but gave no further details. Justice Minister Bekir Bozdag put the number of wounded at 147.
The attack prompted the suspension of all flights at the airport -- one of Europe's busiest hubs.
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Turkish President Recep Tayyip Erdogan called for an international "joint fight" against terror, as Western allies including the United States condemned the "heinous" attack.
Yildirim said the suicide bombers had arrived in a taxi and opened fire on passengers with automatic rifles before blowing themselves up.
Security camera footage widely circulated on social media appeared to capture two of the blasts. In one clip a huge ball of flame erupts at an entrance to the terminal building, scattering terrified passengers.
Another video shows a black-clad attacker running inside the building before collapsing to the ground -- apparently felled by a police bullet -- and blowing himself up.
Roads around the airport were sealed off for regular traffic after the attack and several ambulances could be seen driving back and forth. Hundreds of passengers were flooding out of the airport and others were sitting on the grass. Hevin Zini, 12, had just arrived from Duesseldorf, Germany, with her family and was in tears from the shock.
"There was blood on the ground," she told The Associated Press. "Everything was blown up to bits... If we had arrived two minutes earlier, it could have been us."
South African Judy Favish, who spent two days in Istanbul as a layover on her way home from Dublin, had just checked in when she heard an explosion followed by gunfire and a loud bang.
She says she hid under the counter for some time.
Favish says passengers were ushered to a cafeteria at the basement level where they were kept for more than an hour before being allowed outside.
The private DHA news agency said the wounded, among them police officers, were being transferred to Bakirkoy State Hospital.
An AFP photographer saw bodies covered with sheets at the terminal, which bore heavy damage from the blasts.
Bullet holes peppered the windows and shattered glass lay on the floor, while abandoned luggage was scattered everywhere.
Hundreds of police and firefighters including forensic officers were at the scene.
Tuesday's attack follows coordinated ISIS suicide bombings at Brussels airport and a city metro station in March that left 32 people dead.