The 12,000 personnel who will leave are from the 4th brigade, 82nd airborne and marines battalions, as well as their support staff in the military police, engineers, logistics and transport.
Barack Obama, the US president, has vowed an end to combat operations in Iraq within 18 months, but details of the withdrawal have remained sketchy.
Under a US-Iraqi security pact signed in November during the presidency of George Bush, Obama's predecessor, US troops are to withdraw from towns and cities by June 30 and from the whole country by the end of 2011.
About 140,000 US troops are currently deployed in Iraq, down from a peak of about 160,000 in 2007.
"The successful provincial elections demonstrated the increased capability of the Iraqi army and police to provide security"
General Ray Odierno,
US commander in Iraq
Major-General David Perkins, a spokesman for US forces in Iraq, speaking alongside al-Dabbagh, said that in the coming months 4,000 British troops would also pull out.
The 4,000 British troops due to leave are the last British soldiers in Iraq.
The troop cuts were recommended by General Ray Odierno, the US military commander in Iraq.
"The time and conditions are right," he said in a statement. "The successful provincial elections [on January 31] demonstrated the increased capability of the Iraqi army and police to provide security."
Al-Dabbagh said that the training being provided by US and British troops meant that Iraqi security forces would be able to cope with the situation once foreign troops had left.
"Iraq's armed forces are under construction," he said.
"By 2011 they will be able to stand on their own. We are confident of the fact that the security agreement will be respected."
Security and stability
Security has improved dramatically in Iraq since late 2007 bringing a fragile stability, but attacks remain common across the country.
"The reduction is possible due to the increased level of security and stability that Iraq has achieved over the last 12 months," a statement by the US military said.
However, nearly 260 Iraqis were killed in violence last month, a sharp rise from the previous month that saw the lowest casualty figures since the US-led invasion in March 2003, according to government statistics.
Earlier on Sunday, at least 28 people were killed and dozens more wounded after a suicide bomber on a bicycle attacked a police recruitment centre in Iraq, police said.