Blair will also tell the House of Commons during his regular weekly appearance that a total of about 3,000 British soldiers will have departed southern Iraq by the end of 2007, if the security there is sufficient, the British Broadcasting Corp. said, quoting government officials who weren't further identified.
The British government says this withdrawal is possible because more responsibilities have been handed to Iraqi forces, reports CBS News correspondent Mark Phillips. But Blair has also been under huge political pressure to come up with a withdrawal plan from what has become a very unpopular war.
The announcement comes even as President Bush implements an increase of 21,000 more U.S. troops for Iraq.
But Blair said Sunday that Washington had not put pressure on London to maintain its troop numbers. The BBC said Blair was not expected to say when the rest of Britain's forces would leave Iraq. Britain currently has about 7,100 soldiers there.
Blair's Downing Street office refused to comment on the BBC report.
President Bush spoke with Blair Tuesday morning via secure video, reports CBS News chief White House correspondent Jim Axelrod, and Blair told the president that the withdrawal was a go.
A White House spokesman said the Bush administration would like what's happening with the British troops to be a model for what will eventually happen with U.S. forces, Axelrod reports. In other words, as Iraqi forces are able to handle more of their own security, the need for coalition troops would diminish.
Mr. Bush said Britain's troop cutbacks were "a sign of success" in Iraq.
"The president is grateful for the support of the British Forces in the past and into the future," U.S. National Security Council spokesman Gordon Johndroe said in Washington. "While the United Kingdom is maintaining a robust force in southern Iraq, we're pleased that conditions in Basra have improved sufficiently that they are able to transition more control to the Iraqis.
"The United States shares the same goal of turning responsibility over to the Iraqi Security Forces and reducing the number of American troops in Iraq," Johndroe said. "President Bush sees this as a sign of success and what is possible for us once we help the Iraqis deal with the sectarian violence in Baghdad."
"We want to bring our troops homes as well," Johndroe said. "It's the model we want to emulate, to turn over more responsibilities to Iraqis and bring our troops home. That's the goal and always has been."
Blair said last month that he would report to lawmakers on his future strategy in Iraq following the completion of Operation Sinbad, a joint British and Iraqi mission targeting police corruption and militia influence in the southern city of Basra.
On Sunday, Blair told the BBC that the operation was completed.
Foreign Secretary Margaret Beckett said in January that Operation Sinbad offered the prospect of a "turning point for Iraq, hopefully in the near future."
Treasury chief Gordon Brown, who is likely to succeed Blair by September, has said he hoped several thousand British soldiers would be withdrawn by December.
As recently as late last month, Blair rejected opposition calls to withdrawal British troops by October, calling such a plan irresponsible.
"That would send the most disastrous signal to the people that we are fighting in Iraq. It's a policy that, whatever its superficial attractions may be, is actually deeply irresponsible," Blair said on Jan. 24 in the House of Commons.
Blair, who has said he will step down as prime minister by September after a decade in power, has seen his foreign-policy record overshadowed by his role as Mr. Bush's leading ally in the unpopular war.