The videotape indicated it had been filmed shortly after midday on the day of the attack and showed the bomber giving a speech just before the operation.
Up to 72 people were also wounded in the attack, which targeted a canteen used by US soldiers in the Forward Operating Base Marez in Ghazlani district, southwest of the city of Mosul.
The videotape shows what looks like a map of the camp and the location of the canteen where the explosion occurred.
Some shots showed what appeared to be the planning of the operation, with the hand of an unseen commander pointing out various landmarks on a map of the base.
A masked man, introduced as the bomber, pays tribute to his fellow fighters before heading off to carry out his attack. A voice-over identifies him as Abu Umar al-Mosuli.
Several captives have died in the
Army of Ansar al-Sunna's hands
A statement read out by one of the fighters says al-Mosuli was able to infiltrate into the base "through a breach in the perimeter fence during a changing of the guard, following prolonged surveillance".
Last week, amid speculations about the nature of the attack originally believed to be a rocket or mortar assault, Ansar al-Sunna had said in an unverified website statement it had carried out a "martyrdom operation".