Treasury Secretary Paul O'Neill and White House economic adviser Lawrence Lindsey announced their resignations on Friday.
Officials said their departure from the Bush team was also linked to the president's desire to convince voters that he was addressing their concerns about the ailing economy.
US economic woes were highlighted again on Friday, when it was revealed that unemployment had risen to 6% in November.
"The message is that we are turning over a new leaf here," said one administration official quoted by the New York Times.
Another official described the dismissals as blunt. "We didn't say we want you to take three weeks to think about it," he said.
Mr O'Neill was reportedly told by Vice President Dick Cheney that his services were no longer required.
Bill Archer, a Texas Republican who previously chaired the House Ways and Means Committee, said Mr Bush was "remodelling his team to go into the presidential election" in 2004.
Changes at the top
US administration officials say Mr Lindsey is likely to be replaced by Stephen Friedman, a former chairman of Goldman Sachs Group.
Don Evans, the current Commerce Secretary, has been mentioned as another possible replacement for Mr O'Neill, and Bill Archer and Phil Gramm - another former congressman - are also thought to be contenders.
Mr O'Neill's outspoken style and frank remarks on the economy were sometimes at odds with White House plans, while Mr Lindsey was viewed as a poor spokesman for presidential policy, analysts say.
"Firing its economic team is an overdue admission by the Bush administration that its economic policies have failed," said Senate Democratic leader Tom Daschle.
Poor fit
Mr O'Neill appeared to be content to talk up the economy, while the Bush administration had been looking to accelerate tax cuts to give the economy a boost.
"The suddenness of his departure suggests that he's leaving over some disagreement or battle that he's lost in recent days," Bruce Bartlett, formerly of the US Treasury, told BBC's World Business Report.
"There was a bad fit between Mr O'Neill's style and the administration's style," said Mr Bartlett, who predicted Mr O'Neill's resignation some months ago.
"He has a way of putting things, sometimes, that we call foot-in-mouth disease.
Plain-speaking
Mr O'Neill was sworn in as Treasury Secretary in January 2001, after leaving his post as chairman and chief executive of the aluminium maker Alcoa.
During his time in the post he came under attack for his direct style of speaking.
But he remained unmoved by his critics.
"If people don't like what I'm doing, I don't give a damn," he once said.
His resignation was welcomed by some analysts.
"He's a very able person. But his performance as US Treasury Secretary has not inspired confidence," said Hugh Johnson, chief investment officer at First Albany Corp.
After the surprise resignations the Dow Jones share index fell by more than 100 points in the first few minutes of trade, but then recovered.
Tax reformer
Lawrence Lindsey was one of the driving forces behind the $1.3 trillion tax cut which became the centrepiece of President Bush's election campaign.
But he was criticised, along with Mr O'Neill, for failing to inspire confidence in the economy.
"The economic troubles were being blamed on the messengers, and both O'Neill and Lindsey exuded zero confidence around the country when it came to selling the president's economic agenda," said Republican consultant Scott Reed.