Tony Snow, White House spokesman, said:"We believe Democrats will have control of the House, and look forward to working with Democratic leaders on the issues that remain foremost on the agenda, including winning the war in Iraq and the broader war on terror and keeping the economy on a growth path.
"But it also gets us to a point: Democrats have spent a lot of time complaining about what the president has done. This is an opportunity for them to kind of stand up."
The elections have been shaped by an unpopular war in Iraq, scandal at home and dissatisfaction with George Bush, the president.
Nancy Pelosi, new Democrat speaker in the house, said after the White House announcement: "Staying the course has not made our country safer, has not honoured our commitment to our troops and has not made the region more stable.
"We cannot continue down this catastrophic path. And so, we say to the president: Mr President, we need a new direction in Iraq. Let us work together to find a solution."
Democrat control of the house gives them the power to block and delay many of Bush's policies.
Senate race continues
In the Senate, the other of Congress's two houses, Democrats have taken four of the six seats they need to take control.
However, analysts have said that the Democrats will need to win the remaining two seats in order to take control of the Senate.
"I think we will hold control of the Senate," Ken Mehlman, the Republican national chairman, said on CNN.
The BBC's Jamie Coomarasamy in Washington says the results have changed the political landscape in the US, and the last two years of the Bush presidency will be very different from what has gone before.
With projected results still coming through, the Democrats had gained 16 House seats from the Republicans - enough to win control providing they hold their existing seats.
The Senate hinges on Montana and Virginia, where Democrats must win and are leading in races too close to call - with Virginia facing a likely recount.
House Democratic leader Nancy Pelosi said the American people had "voted for Democrats to take our country in a new direction - and that is exactly what we intend to do".
Ms Pelosi - who stands to become the first female House speaker - said the Democrats would "restore integrity and honesty" to Washington and lead the "most ethical Congress in history".
Presidential spokesman Tony Snow said the White House had admitted defeat in the House.
"We believe Democrats will have control of the House, and look forward to working with Democratic leaders on the issues that remain foremost on the agenda, including winning the war in Iraq and the broader war on terror and keeping the economy on a growth path," he said.
President George W Bush has scheduled a news conference for 1800 GMT.
The speech will provide the first clue as to whether Mr Bush intends to compromise with his newly powerful opponents or fight them, the BBC's Justin Webb in Washington says.
Analysts say control of the House will allow Democrats to choose to launch inquiries into the handling of Iraq, and could lead to significant changes on domestic issues like taxation and health care.
Democratic hopes have been bolstered by wins bringing them closer to their target of six net Senate seats.
However, the Senate race in Virginia, where Democrat Jim Webb is challenging incumbent George Allen, is likely to go to a full recount, correspondents say.
The race remained neck-and-neck after Bob Corker held on to the Republicans' Senate seat in Tennessee, despite a strong challenge from Harold Ford Jr.
In other results:
- In Pennsylvania, Democrat Bob Casey Jr beat one of his party's biggest Republican targets this year, arch-conservative incumbent Rick Santorum
- In Ohio, where the Republican Party has been hit by scandal, Democrat Sherrod Brown won a decisive victory over incumbent Republican Mike DeWine
- The Senate seat in Rhode Island went to Democrat Sheldon Whitehouse after a closely-fought battle with incumbent Republican Lincoln Chafee
- In New Jersey, Democrat incumbent Senator Bob Menendez succeeded in holding off a strong challenge from the Republicans' Thomas Kean. The race had been seen as the Republicans' best chance of picking up a seat from their rivals
- The Senate seat in Connecticut has gone to Joe Lieberman, who stood as an independent after losing the Democratic primary to Ned Lamont amid strong anti-war feeling. He has said he will align himself with the Democrats
- Democrat Keith Ellison was elected as the nation's first Muslim member of Congress, taking a House seat in Minnesota
- Democratic Senator Hillary Rodham Clinton has strolled to re-election in New York, as expected. Her win opens the way for a potential presidential run in 2008
- Republicans lost the Florida district of Mark Foley, who resigned after the disclosure that he sent sexually explicit messages to teenage male congressional assistants.
"It's been kind of tough out there," said Republican House speaker Dennis Hastert, who won a 11th two-year term.
While Mr Hastert won his district, he will lose his job as speaker after the Republicans lost control of the House of Representatives.
PRE-VOTE CONGRESS BALANCE
HOUSE OF REPRESENTATIVES:
435 seats - all being contested
Republicans hold 229 seats; Democrats 201; one seat independent; four vacant seats
Democrats need to win net 15 seats to win control of House
100 seats - 33 being contested
Republicans hold 55 seats; Democrats 44; one independent
Democrats need to win net six seats to win control of Senate
Voters were also choosing governors in 36 states.
Democrat Deval Patrick has taken the governorship in Massachusetts, becoming the first black governor of the state and only the second elected black governor of any state.
In some good news for the Republicans, Arnold Schwarzenegger has held on to his gubernatorial seat in California for a second term.
And in one of a series of state referendums, voters in South Dakota have overturned a near-total ban on abortions passed by the state legislature earlier this year.
A high turnout was reported in Tuesday's vote.
A national exit poll for the Associated Press indicated that about two-thirds of people felt Iraq was very important to their vote.
Yet even more voters - about 80% - said the economy, government corruption and scandal were very important to their votes, the survey of 8,344 voters said.
Technical hitches delayed voting in dozens of precincts in Indiana and Ohio.
Officials extended polling hours in six states because of problems with electronic voting machines.
The new voting technology was brought in to replace older systems, such as the punch-card machines which were at the centre of the Florida dispute during the 2000 presidential election.
In Virginia, election officials told ABC News the FBI was investigating claims of voter intimidation.