Acting on recommendations made by Defense Secretary Robert Gates, the president announced the withdrawal of 8,000 troops from Iraq by next February: A battalion of 1,500 Marines out of western Iraq in November, and an Army combat brigade of 3,500 soldiers in February, along with 3,400 support troops.
That will bring overall troop strength in the country down to 136,000 - about what it was in 2006 before the "troop surge" was announced.
Mr. Bush also announced an increase in U.S. forces in Afghanistan: A Marine battalion that was scheduled to deploy to Iraq in November will instead be shipped to Afghanistan, and an Army combat brigade will follow in January.
CBS News national security correspondent David Martin said the troop withdrawal could well be Mr. Bush's last major decision on the Iraq War - an issue that has dominated and defined his presidency.
But even these modest withdrawals - less than six percent of U.S. troops - are more than the commander in Iraq, General David Pretraeus originally wanted; he recommended no further reductions until June of next year.
But he was overruled because of the pressing need to free up more troops for Afghanistan.
Still, Martin notes, the 5,000 additional forces headed for Afghanistan is only a fraction of what the commander there says he needs.
Speaking this morning to an audience at the National Defense University in Washington, D.C., Mr. Bush held up Iraq's Anbar province - the site of the 2006 Anbar Awakening - as evidence of the success of the U.S. troop surge that was instituted last year.
"Anbar was one of the most dangerous provinces in Iraq," he said. "Al Qaeda was in control of almost every major population center."
He said military intelligence had concluded the province was lost.
"Anbar was held up as proof of America's failure in Iraq," he said. "Yet something remarkable was happening. The tribes in Anbar were growing tired of al Qaeda's brutality. They wanted to live a normal life, and this presented us with an opportunity to defeat al Qaeda in Anbar."
He said the 4,000 additional Marines who went to Anbar last year showed America's commitment to security there. "It helped renew the confidence of local leaders, the tribal sheiks who led an uprising to take Anbar back from the terrorists. Together [the insurgents] were systematically controlled.
"Today Anbar is a province transformed."
Mr. Bush said the recent turnover of control to Iraqi authorities in Ramadi is evidence that Iraq is on the road to self-governance and self-defense.
Mr. Bush then turned his focus to Afghanistan, where U.S. casualties have been increasing, and where a "quiet surge" (his term) of U.S. Marines and NATO troops, and a doubling of trained Afghan security forces, has been taking place in recent months.
He also spoke of- Afghanis who have lost their lives in the midst of U.S. and NATO operations.
"Regrettably there will be times when our pursuit of the enemy will result in accidental civilian deaths. This has been the case throughout the history of warfare. Our nation mourns the loss of every innocent life. Every grieving family has the sympathy of the American people. I've given President Karzai my word that America will work closely with the Afghan government to ensure security of Afghan people while protecting innocent lives."
Mr. Bush said the additional troops will be employed to provide security, protect the country's infrastructure and democratic institutions and help ensure access to services like education and health care.
"Afghanistan's success is critical to the security of America and our partners in the free world. For all the good work we've done in that country, it is clear we must do even more. As we learned in Iraq, the best way to restore the confidence of the people is to restore basic security, and that requires more troops."
He also announced an allied initiative to double the size of the Afghan
National Army over the next five years, and to increase the involvement of local tribes.
"In the period ahead we will once again encourage Afghan security forces and Afghan tribes to take a leading role in the building of a democratic Afghanistan. The Taliban and al Qaeda will not be allowed to return to power. The terrorists will suffer the same fate in Afghanistan that they are now suffering in Iraq, and they will be defeated."