"We have agreed that a total of 12,000 US troops will be withdrawn by the end of September 2009," government spokesman Ali al-Dabbagh said, adding that 4,000 British forces would leave in July.
Under a US-Iraqi security agreement signed in November, US troops are to pull out of towns and cities by June 30 and from the whole country by the end of 2011.
Some 140,000 US troops are currently deployed in Iraq -- down from a peak of more than 160,000 during the 2007 "surge" offensive against insurgents and Al-Qaeda.
The announcement came just hours after a suicide bomber on a bicycle blew himself up killing 28 people and wounding 58 more outside a Baghdad police academy in the bloodiest attack in weeks, officials said.
The bomber activated an explosive vest as he ploughed into the crowd on busy Palestine Street in the city centre, an interior ministry official said.
"The majority of the dead were police or recruits," the official said.
Police academies across Iraq have come under repeated attack, the latest coming at the same academy on December 1, when at least 15 people died.
It is located in a high security area which includes the interior and oil ministries as well as army and national police compounds.
In August, 25 Iraqis -- most applicants to the police force -- died in a suicide bombing at a recruiting centre in Diyala province, northeast of Baghdad.
Security had been stepped up at the Baghdad academy and access to the building is intended to be only on foot through checkpoints.
Despite ongoing security concerns, Iraqi spokesman Dabbagh said: "The government has no intention of keeping foreign forces in the country after 2011.
"Iraq's armed forces are under construction," Dabbagh added, next to coalition forces spokesman Major General David Perkins of the US army.
"By 2011 they will be able to stand on their own. We are confident of the fact that the security agreement will be respected."
Perkins said the US forces would be reduced from 14 to 12 brigades -- two combat brigades, including the 4th brigade, 82nd airborne and marines battalions, as well as their support staff.
An F16 squadron would be pulled out too and not be replaced.
"We will not leave any seams with regard to security," Perkins said. "We know how to do this. This is not the first time we have done this."
US President Barack Obama has announced an end to combat operations in Iraq within 18 months, but details of withdrawals had remained sketchy.
US counter-terrorism and training forces numbering up to 50,000 are to remain in Iraq until a full withdrawal by the end of 2011.
British Prime Minister Gordon Brown visited Iraq in December and announced the 4,100 British troops would leave by the end of July, but their mission is expected to finish at the end of May.
The American troop cuts were recommended by the senior US military chief in Iraq, General Ray Odierno.
"The time and conditions are right," Odierno said in a statement. "The successful provincial elections (on January 31) demonstrated the increased capability of the Iraqi army and police to provide security.
"In the coming months, Iraqis will see the number of US forces go down in the cities while more and more Iraqi flags will go up at formerly shared security stations."
Security has improved dramatically in Iraq since late 2007 bringing a fragile stability, but attacks remain common in the country.
Sunday's suicide blast followed a truck bomb that killed 10 people and wounded more than 50 on Thursday at a crowded livestock market in central city of Hilla.
Asked about the latest bombings, Perkins said, "Most of them have the typical al-Qaeda signature."
"Al-Qaeda and other terrorists are still active, they're trying to maintain relevance.
"They have much less capability, the numbers of attacks were dramatically low, however they're still there."
Sunday's blast was the deadliest since a suicide bomber killed 35 pilgrims heading to the shrine city of Karbala south of Baghdad on February 13.
Some 258 Iraqis were killed in violence last month, up on the 191 people killed in January, which itself was the lowest casualty figures since the US-led invasion in March 2003.
A total of 4,556 US soldiers have died in Iraq over the past six years as well as 179 British soldiers.