The US president has nominated Rob Portman, the trade representative, as the White House budget director, turning to a Washington insider as part of an effort to re-energise the administration.
The move is being seen by many analysts as an attempt to boost the president's record-low opinion poll approval ratings.
Also on Tuesday, Bush selected Susan Schwab, the deputy trade representative, to move up as Portman's replacement.
As one of three deputies to Portman, Schwab is responsible for developing, negotiating and implementing trade policy for Europe, Eurasia, the Middle East and the Western hemisphere.
She also is responsible for the operations of the trade representative's office involving the World Trade Organisation and other multilateral affairs including intellectual property and industry, market access and telecommunications.
Bush said more changes are in the works under his new chief of staff, Joshua Bolten.
"With a new man will come some changes," the president said.
Bush again emphasised that Donald Rumsfeld's job as defence secretary is safe despite calls for his resignation from a half-dozen retired military commanders.
"I hear the voices, and I read the front page, and I know the speculation," he said.
Ex-Ohio congressman Portman
(L) is a confidant of Bush
"But I'm the decider, and I decide what's best. And what's best is for Don Rumsfeld to remain as the secretary of defence."
The president noted that Washington is buzzing with rumours about an administration shake-up.
John Snow, the treasury secretary, is said to be on the verge of leaving, and Republicans outside the White House say they expect changes in the White House lobbying and communications shops.
"I understand this is a matter of high speculation here in Washington," Bush said.
"It's the game of musical chairs, I guess you would say, that people love to follow."
Bush said he had given Bolten broad authority to make changes to strengthen the White House.
"And of course he will bring different recommendations to me as to who should be here and who should not be here," Bush said.
Rumsfeld has been assured that
his job is safe
Tuesday's appointments were the first major personnel changes since Bolten took over and said he wanted to re-energise and recharge Bush's troubled presidency.
With the Iraq war in its fourth year, Bush's poll ratings are at their lowest point and Republicans are anxious about the November elections.
Bolten, at his first senior staff meeting on Monday, pointed towards more personnel changes.
He said that staff who were thinking about leaving before the end of the year should go now.
Portman, a former Republican congressman from Ohio, is a confidant of Bush and has experience in Washington.
As a member of the tax-writing House Ways and Means Committee and as vice chairman of the Budget Committee, Portman forged bipartisan coalitions on legislation dealing with tax, trade and pension reform policy.
A year ago, Bush nominated Portman to succeed Robert Zoellick as his top trade negotiator.
Portman pledged during his confirmation hearings last year to take a tougher line with China, and in February his office produced a top-to-bottom review of US relations with China.
The administration is expected to use the review to push for more trade concessions when Bush meets Hu Jintao, the Chinese president, on Thursday at the White House.