The president's decisions amount to perhaps his last major troop strategy in the war that has come to define his presidency.
He was to announce the details in a speech Tuesday, the text of which was released in advance by the White House.
One Marine battalion, numbering about 1,000 troops, will go home on schedule in November and not be replaced. An Army brigade of between 3,500 and 4,000 troops will leave in February. Accompanying that combat drawdown will be the withdrawal of about 3,400 support forces.
The measured reduction - slower in scope and pace than many Democrats in Congress would like - gives the military some flexibility to shift forces into Afghanistan.
"Here is the bottom line: While the enemy in Iraq is still dangerous, we have seized the offensive, and Iraqi forces are becomingly increasingly capable of leading and winning the fight," Bush said in remarks prepared for delivery to the National Defense University in Washington.