Approval by the presidential council came one week after parliament approved the agreement, which was hammered out during months of tough negotiations that at times seemed on the point of collapse.
But the pact, which commits Washington to withdraw its forces by December 31, 2011, is still subject to approval by Iraqi voters in a referendum by the end of July next year.
If voters reject the deal, Iraq will ask the US for a new round of talks.
The presidential council approval came as suicide bombers killed 17 people and wounded nearly 150 in Falluja.
A senior police officer said explosives-laden lorries were detonated near concrete barriers surrounding two separate police stations in Falluja on Thursday.
A school near one of the posts collapsed following the explosion, an interior ministry official said, injuring several schoolchildren.
Falluja is one of the main cities in al-Anbar province, which was the centre of the Sunni-led fight against US forces in the months following America's March 2003 invasion.
Also on Thursday, two US soldiers were killed and nine Iraqis wounded in a suicide car bombing in the northern city of Mosul.
Elsewhere in northern Iraq, four fighters were killed and dozens detained in US operations targeting al-Qaeda in the north of the country, the US military said.