Bush also defended the move to oust the Iraqi leader - later tried and hanged in Iraq by the US-backed government - as "the right decision then, and ... the right decision today".
Troops from the 101st Airborne will be deployed in Afghanistan in the coming weeks, in a sign of the shifting focus of US military strategy from Iraq to Afghanistan - shared by Bush and Barack Obama, the US president-elect.
Last week Iraq and the US signed a security accord requiring Washington to withdraw its forces from the country by the end of 2011.
The Status of Forces Agreement (Sofa) pact was signed last week by Hoshyar Zebari, the Iraqi foreign minister, and Ryan Crocker, the US ambassador, at a ceremony in Baghdad, the Iraqi capital.
It now goes to the Iraqi parliament on Wednesday, where US officials say they are "hopeful" it will pass.
The move followed fraught negotiations between Washington and Baghdad over the pact, which replaces a United Nations mandate due to expire in December.
Sticking points included the rule of law over US troops and civilian contractors on Iraqi soil and assurances that the US military would not use Iraqi territory as a base to launch attacks on neighbouring countries such as Iran and Syria.
The Bush administration, which initially opposed any firm timetable for withdrawing US forces in Iraq - says the latest version of the agreement shows the Iraqis wish to govern and defend themselves following Saddam Hussein's removal in 2003.
"The Iraqis have come a long way, but they're not quite there yet to be able to take care of all their security needs on their own ... They continue to need our support," Dana Perino, the White House spokeswoman, said on Tuesday.