A video posted today on a website showed the beheading purportedly carried out personally by key terror suspect Abu Musab al-Zarqawi.
The video showed Armstrong sobbing and blindfolded wearing an orange jumpsuit.
Five militants dressed in black stood behind Armstrong, who was identified after an earlier video announcing his abduction.
Four of the militants were armed and a Tawhid and Jihad banner hung on the wall behind them.
The man in the centre, believed to be al-Zarqawi, read out a statement.
He threatened to take the life of another hostage in 24 hours if London and Washington continued to ignore demands for the release of Iraqi women prisoners in coalition custody.
He then appeared to pull a knife, rushed to the hostage from behind and cut his throat until the head was severed.
He held up the head and placed the head on top of the body.
Armstrong and British engineer Kenneth Bigley and fellow American Jack Hensley were abducted from their Baghdad home on Thursday.
All three worked for a contracting firm Gulf Supplies and Commercial Services.
The video was shown on the Islamist website in the name of the Unity and Holy War group of suspected Al-Qaeda operative al-Zarqawi.
The authenticity of the nine-minute tape cannot be verified.
But the voice of the militant reading a statement sounded like past recordings said to be of al-Zarqawi.
The US government has confirmed that it has recovered Armstrong's body in Iraq.
Meanwhile a man's body has been discovered in northern Iraq with bullet wounds in his chest.
Police said documents found next to the naked body indicated the man was from the Turkish city of Mardin.
The body was found near the town of Ash Sharqat, 270 kilometres north of Baghdad.
Police said the circumstances and motive behind the man's killing were not clear.