"And if the progress in Iraq continues to hold, General [David] Petraeus and our military leaders believe additional reductions will be possible in the first half of 2009."
No large-scale shift
A cut of 8,000 would leave 138,000 US troops in Iraq.
That will still be more than before Bush ordered a "surge" of extra forces in 2007 and also more than in November 2006, when his Republicans lost mid-term congressional elections largely due to voter anger over the war.
Bush's plan follows recommendations from senior US defence officials, including Robert Gates, the defence secretary, Mike Mullen, chairman of the joint chiefs of staff and David Petraeus, the top commander in Iraq.
Obama has promised to withdraw US troops from Iraq within 16 months and said he would put more resources into Afghanistan and "anti-terrorism efforts" along the Pakistan border, where US officials say they believe Osama bin Laden, the al-Qaeda leader, is hiding.
McCain has refused any set any timeline for withdrawing troops from Iraq.
He has said he prefers Bush's policy of removing them based on commanders' recommendations and security conditions in the war zone.
Bush, in his speech on Tuesday, will point to data showing violence in Iraq has dropped to levels not seen since 2004.
'Fragile and irreversible'
But he will caution that "progress" in Iraq, which US-led forces invaded in March 2003 to remove Saddam Hussein, remains "fragile and reversible".
Bush's "surge" strategy, which sent an additional 30,000 troops to Iraq, has helped stem violence and pulled Iraq back from the brink of civil war, according to White House officials.
The so-called "surge," which was announced in 2007, was criticised by many Democrats who said the US should be pulling out of the country.
About 20,000 of the "surge" troops have returned home without replacement, leaving 146,000 US troops in Iraq.
Bush will say about 3,400 support troops will leave Iraq over the coming months, along with a marine battalion by November.
But while violence has fallen in Iraq, attacks against US, Nato and Afghan troops in Afghanistan have soared.
Nato commanders there have asked for additional forces for years and say they still need about 12,000 troops.
The US has 33,000 troops in Afghanistan, split between a Nato-led mission and a separate "counter-terrorism" mission run by the Pentagon.