The Red Cross said at least 239 people were also wounded, several in critical condition, in the blasts that hit a busy shopping street in the Burj al-Barajneh neighbourhood, where the Shiite Hezbollah movement is popular.
The attack harked back to a campaign against the group between 2013 and 2014, ostensibly in revenge for its military support of regime forces in neighbouring Syria's civil war.
But it was the largest attack ever claimed by IS in Lebanon, and among the deadliest bombings to hit the country since the end of the 1975-1990 civil war.
Schools were closed for the day, and politicians across Lebanon's fractured political spectrum offered condemnations of the attack.
More From This Section
The blasts ripped through a street market in the poor, mainly Shiite Muslim neighbourhood, staining the ground red with blood and gutting several surrounding shops.
The army said the attack was carried out by two suicide bombers, and that the body of a third who failed to detonate his explosive device was found at the scene of the second blast.
It said "soldiers of the Caliphate" first detonated explosives planted on a motorbike on the street.
"After the apostates gathered in the area, one of the knights of martyrdom detonated his explosive belt in the midst of them," the statement added.
It made no reference to Hezbollah's involvement in Syria, much of which is under IS control, instead using starkly sectarian language and derogatory terms for Shiite Muslims.
The Sunni extremist group considers members of the sect, as well as others who stray from its interpretation of Islam, to be apostates.
Local television stations showed footage after the blast of the wounded being carried away.
"I carried four bodies with my own hands, three women and a man, a friend of mine," a man who gave his name as Zein al-Abideen Khaddam told local television.
Another described the sound of the explosions: "When the second blast went off, I thought the world had ended.