Four other US soldiers and an Iraqi interpreter were killed during the ambush.
The US military said late last month that Anzack's body was found floating in the Euphrates river and it was still searching for the other two soldiers.
The video, obtained by news agencies from the US-based SITE Institute, shows a group of masked men apparently planning the ambush using a diagram pinned to a tree.
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This is followed by night footage of the attack and daylight images of the aftermath taken from Al Jazeera.
Personal items belonging to the soldiers are also shown, including a pistol, credit cards, and US and Iraqi currency.
"They (the Islamic State of Iraq) ... announced the news of their killing to cause bitter results upon Allah's enemies, with these three soldiers, from being live prisoners to dead bodies," said a speaker on the video.
"Fearing the occupying army will continue its searches, harming our Muslim brothers ... (the Islamic State in Iraq) decided to settle the matter and announced the news of their killing to cause bitterness to God's enemies."
Websites often used by al-Qaeda-linked groups said earlier on Monday they would soon show the abduction of three Americans, apparently referring to three US soldiers who went missing in Iraq last month after a clash.
A voice on the video said that it would not deliver the bodies of the two soldiers, saying "their end will be underneath the ground, Allah willing".
There was no footage of the soldiers.
Brigadier-General Kevin Bergner, a spokesman for the US-led multinational force in Iraq, said: "We are further analysing the video. However, it doesn't appear to contain any definitive evidence indicating the status of our missing soldiers.
"We continue to search and hope our two missing soldiers will be found alive and in good health.
"We condemn the tactics used by these terrorists and are using all means available to pursue those responsible."