The US was not allowed to carry out air strikes from Saudi Arabia
The United States has said that virtually all its troops, except some training personnel, are to be pulled out of Saudi Arabia.
The decision was confirmed by US Defence Secretary Donald Rumsfeld during a joint news conference with Saudi Defence Minister Prince Sultan.
Both men stressed that there were no differences between their countries and their co-operation would continue.
Ever since the 1991 Gulf war, the US has had about 5,000 troops stationed in Saudi Arabia - a figure that rose to 10,000 during the recent conflict in Iraq.
The BBC's Middle East analyst Roger Hardy says this is a strategic shift of great political as well as military significance.
Technically US troops there have been part of Operation Southern Watch, which has enforced the no-fly zone over southern Iraq set up after 1991.
But our correspondent says the US troops have become a potent symbol of Washington's role in the region, and many Saudis see them as proof of the country's subservience to America.
Saudi Arabia is home to some of Islam's holiest sites and the deployment of US forces there was seen as a historic betrayal by many Islamists, notably Osama Bin Laden.
Bin Laden used American presence to justify anti-US attacks
It is one of the main reasons given by the Saudi-born dissident - blamed by Washington for the 11 September attacks - to justify violence against the United States and its allies.
But news of the US pull-out does not mean the campaign is over for Bin Laden and his followers, according to the BBC's Arab affairs analyst Magdi Abdelhadi.
Their agenda now goes beyond the boundaries of one country, he says. Their goal is to liberate all Muslim societies from foreign troops and what they see as ungodly secular rulers.
The al-Qaeda leader was expelled from Saudi Arabia in 1991 because of his anti-government activities.
In other developments:
- The US says it will deploy up to 4,000 additional troops to boost security in Baghdad
- US forces in the Iraqi town of Falluja open fire on protesters, reportedly killing at least 13
- The governor of Basra under Saddam Hussein has surrendered in Baghdad, according to the Iraqi National Congress.
Earlier on Tuesday, the US military confirmed that it was moving its air command centre from Saudi Arabia to the al-Udeid air base in neighbouring Qatar.
US Rear Admiral David Nichols said the Combined Air Operations Centre (CAOC) at the Prince Sultan base in Saudi Arabia would be closed by the end of the summer.
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"We already have switched, as of yesterday (Monday)," Admiral Nichols said.
But, he added, the base would remain wired and could be used again if the US and Saudi Arabia decided it was necessary.
The CAOC was set up after the 1991 Gulf war in Iraq and was used to control the coalition air campaign in the latest conflict in Iraq.
Mr Rumsfeld - who is touring the Gulf region to thank US troops and regional allies - said the US was grateful for the "co-operation and support" provided by Saudi Arabia.
The Saudi defence minister said that, since US and British patrols over the Iraqi no-fly zones had ended, there was "no need" for the American forces to be there.
"This does not mean we have requested them to move," he said.
"The co-operation between our two countries was going on even before Desert Storm and it will continue even after the end of the war in Iraq."
In the run up to the US-led invasion of Iraq, the Saudis said they would not allow American planes to carry out air strikes from the Prince Sultan base without a UN resolution authorising war.
The Saudi refusal was reported to have created a rift between Riyadh and Washington.