Mr Bush (right) will endorse Gen Petraeus' proposals, officials say
They say the cuts, with conditions attached, will be announced by the president in a major TV address.
The move would bring the number of US troops in Iraq to "pre-surge" levels.
The US top military commander in Iraq and the US envoy in Baghdad have told Congress that the surge, launched in February, is working.
President Bush will make the speech on Thursday night at 2100 local time (0100GMT on Friday).
It sounds to me as if Gen Petraeus is presenting a plan for at least a 10-year, high-level US presence in Iraq
Nancy Pelosi (D) House of Representatives Speaker
Key quotes: Second day Mid-East media on findings
The White House says it will contain an endorsement of the troop reduction proposed by Gen David Petraeus, who has been testifying in Congress on Monday and Tuesday.
However, Mr Bush is expected to condition his plans - and also further troop cuts - on continued progress in Iraq.
The BBC's Justin Webb, in Washington, says the president's move is an attempt to seize the initiative and to give the impression - whether true or not - that he is driving events.
Surge hearings
Gen Petraeus - and also US envoy in Iraq Ryan Crocker - faced severe criticism during the two days of their testimony in Congress from lawmakers opposed to the war.
Sen Joseph Biden (D) - who chairs the Foreign Relations Committee - said on Tuesday that the surge had failed to promote reconciliation between Sunnis and Shia, and was at best "a stopgap that will not prevent chaos".
House of Representatives Speaker Nancy Pelosi (D) said: "It sounds to me as if Gen Petraeus is presenting a plan for at least a 10-year, high-level US presence in Iraq."
Gen Petraeus said that violence in Iraq had declined significantly since February, but stressed that a premature troop reduction would have "devastating consequences".
A record 168,000 US troops are now in Iraq after 30,000 arrived in the surge between February and June.
According to United States officials at the White House, President George W. Bush will be cutting the amount of U.S. troops in Iraq by as much of 30,000, to "pre-surge" force levels, and the withdraw could take place as early as next Summer, but with certain "conditions" applying.

The plans are expected to be formally announced in a speech Bush is expected to make on Thursday at 9:00 p.m. (eastern time).

Officials say that the President will endorse the reduction of troops recommended by General David Petraeus.

"I believe that we will be able to reduce our forces to the pre-surge level ... by next summer without jeopardizing the security gains we have fought so hard to achieve. The level of security incidents has declined in eight of the past 12 weeks, with the level of incidents in the past two weeks the lowest since June of 2006," said Petraeus while testifying in front of the U.S. Congress on Monday.

According to officials, the conditions on the reduction of troops depends on whether or not violence in Iraq continues to decline, and how much political stability and security progresses.

Currently, there are 168,000 U.S. troops serving in Iraq, the most that have ever been in the country.