The two leaders made the announcement in a joint statement released as they held talks in Baghdad.
They said: "The role played by the UK combat forces is drawing to a close. These forces will have completed their tasks in the first half of 2009 and will then leave Iraq."
Mr Brown said that British operations In Iraq would finish by May 31st 2009. The vast majority of British troops will return before the end of July.
"We have agreed today that the mission will end no later than the 31st of May next year," Mr Brown said. "Our troops will be coming home within the next two months (after that)."
He went on: "The biggest reduction will be at the end part of the period we are talking about."
Mr Maliki confirmed that the agreement included a provision for the Iraqi government to request an extension of the British military presence. However, both leaders indicated that it was not expected to be used.
On Tuesday the Iraqi council of ministers agreed a new resolution allowing British troops to remain in the country until the end of July. Their current United Nations mandate expires at the end of the month.
British officials say the resolution merely set a last possible date for the vast majority of Britain's 4,100-strong contingent to be gone.
Mr Brown confirmed the outlines of the plans before preparing to update the House of Commons in greater detail on Thursday.
The Prime Minister is being accompanied on the visit by the Air Chief Marshall Sir Jock Stirrup, the Chief of the Defence Staff.
Mr Brown's visit to Iraq follows a similar pre-Christmas trip to Afghanistan at the weekend.
Mr Brown is hoping that British troops will begin withdrawing from their base in Basra in the Spring.
There are still more than 4,000 British troops in Iraq and this number is expected to be reduced to just a few dozen by the summer.
During the visit, it is understood that Mr Brown has travelled outside of the heavily-secured green zone in central Baghdad for the first time. The Prime Minister believes this demonstrates the major developments that have been made in improving security in Iraq in recent months.
The Prime Minister is also expected to use the visit to raise the plight of five Britons who are still being held hostage in Iraq.
The withdrawal of troops from Iraq will mark the end of an important chapter in recent military history. More than 42,000 troops were involved in the invasion of Iraq. 178 British service personnel have lost their lives during the conflict.
