"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.
But any large-scale shift in US forces in Iraq and Afghanistan will be left to Bush's successor - either John McCain, the Republican nominee or Barack Obama, the Democratic candidate.
Bush will leave office in January 2009 after the November 4 presidential elections.
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 timeline for withdrawing troops from Iraq.
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 added about 30,000 troops to Iraq, has been credited with helping to stem violence and pulling Iraq back from the brink of civil war.
The surge, which was announced in 2007, was criticised by many Democrats who said the US should be pulling out.
About 20,000 of those surge troops have returned home without replacement, leaving 146,000 US troops in Iraq.
Bush will say some 3,400 support troops will leave Iraq over the coming months, along with a marine battalion by November.
But as 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.