As an architect of the war that ousted Saddam Hussein, Rumsfeld symbolised a policy under heavy attack due to unrelenting violence in Iraq. It was a major factor in losses by Bush's Republicans in congressional elections on Tuesday.
His replacement with former CIA boss Robert Gates signals a change in direction. Gates is a member of the Iraq Study Group, a bipartisan panel reviewing US policy expected to produce recommendations in the coming weeks.
Some analysts expect the group, co-chaired by Republican former Secretary of State James Baker and Democratic former Rep. Lee Hamilton, to back a phased withdrawal of US troops in Iraq, who currently number around 152,000.
More than 2,800 US troops and at least tens of thousands of Iraqis have died since the US-led invasion in 2003.
"The fact that Rumsfeld not only went but that Gates came in says to me that what you're going to see is some sort of phased withdrawal," said Lawrence Korb, an assistant secretary of defence under President Ronald Reagan.
"You'll cut down the number of troops gradually to tell the Iraqis that the United States is not going to be there for ever and they're gonna have to get their act together," said Korb, now with the Center for American Progress think tank.
Until now, US officials have said troops will stay in Iraq as long as needed to drive down violence and train Iraqi forces to provide security.
Loren Thompson from the Lexington Institute, another Washington-area think tank, said he also expected a drawdown.
"I think there's no question that the size of the American commitment to Iraq will be scaling back," he said. "The only question is what the schedule of that shrinkage will be."
Although Rumsfeld announced his resignation on Wednesday, he remains in office until Gates is confirmed by the Senate.

'CAN'T-WIN SITUATION'
Earlier in their mission, US forces in Iraq struggled with a Sunni Muslim insurgency and attacks by al Qaeda militants but commanders say the most serious problem is now deadly sectarian violence between Sunnis and Shias.
With security deteriorating so much since the invasion, many analysts believe the United States now has no good options in Iraq. The best scenario they see is keeping some sort of check on the violence, the worst is a full-scale civil war.
"Rumsfeld is leaving US forces in Iraq in a can't-win situation," Thompson said.
Advocates of a phased withdrawal hope it would push Iraq's government to take more responsibility for security and take measures to foster reconciliation among competing factions.
But Tom Donnelly of the Center for Strategic and International Studies said that while US forces had improved counter-insurgency capabilities, it was not clear anyone had come up with a good plan to deal with the sectarian violence.
He suggested US officials may have to "accept the fact there's a civil war and ... figure out who you want to be victorious in that civil war".
He said hopes that Gates, an intelligence and national security specialist, would come up with a winning military strategy could be misplaced.
"He's not a guy with a defence background," Donnelly noted. He said Bush, as the commander in chief who took the United States into the war, would be the key decision-maker.
"The president will have the whip hand," he said.

Copyright Reuters, 2006