While the Democrats oppose Bush's strategy, they have been wary of cutting funding to the war in Iraq.
In his speech, Bush also said that the US would hold the Iraqi government to certain "benchmarks", including the passage of oil-sharing legislation, reconstruction and job projects, and political reforms.
Analysts said Bush's speech on Wednesday was more about the president's place in history than American politics.
Bruce Buchanan, a political analyst at the University of Texas, said: "We are seeing a president defying public opinion in a way that no modern president has.
"He has his eye on history. His most important jury is not the public but historians.
"For him, this is the defining issue of our times and he's hell-bent on avoiding surrender."
Opinion polls show declining public confidence in Bush's conduct of the war, with the majority opposed to his proposal to send more troops to secure Baghdad.
A USA Today/Gallup poll said Americans oppose the idea of increasing troop levels in Iraq by 61 per cent to 36 per cent.
"We are seeing a president defying public opinion in a way that no modern president has"
Bruce Buchanan, political analyst
The decision also come just two months after the Democratic election victory, which was seen as a rejection of his Iraq policy.
The move is seen as a final attempt to turn around an increasingly unpopular war that many say will define Bush's legacy as president.
Analysts also said that Bush's decision would badly affect the Republican party.
Because of the promise of nonbinding votes from the Democrats in congress on the proposal, Republicans will be forced to choose between breaking with Bush or embracing an unpopular policy in the build up to elections in 2008.
"Obviously there is tremendous scepticism in the public about where this policy is going, and Republicans will be the ones to pay any price," said Andrew Taylor, a political analyst at North Carolina State University.
Senior administration officials said 17,500 troops would go to Baghdad and 4,000 to Anbar province, with the first wave of troops expected to arrive in five days.
"Bush's strategy has failed totally in Iraq and USA has already lost the war. The new plan will not work; it will only bring more deaths and make things in Iraq worst..."
Dimos, Hania-Crete, Greece
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Others will come in additional waves, joining about 130,000 already in Iraq.
Under the plan, the Iraqi government will deploy additional Iraqi troops to Baghdad with a first brigade deploying on February 1 and two more by February 15.
The troops will follow a chain of command leading to Nuri al-Maliki, the Iraqi prime minister.
Bush is calling for turning over security of all Iraqi provinces by November, but officials caution that this did not represent a timetable for a US pullout.
Iraqis currently control only three of 18 provinces.
Bush also acknowledged mistakes that had been made in Iraq and said that more US and Iraqi troops should have been used in military operations.
More than 3,000 US troops have died in Iraq since the US-led invasion in March 2003 to topple Saddam Hussein and dismantle his supposed weapons of mass destruction.
Hoshyar Zebari, the Iraqi foreign minister, interviewed on Al Jazeera on Wednesday, said: "The plan is that Iraqi forces will take the lead in the cleaning-up of streets and neighbourhoods of Baghdad ... that's how this plan differs from previous plans. This plan will not discriminate. "
The plan will cover all those neighbourhoods that have been a source of violence, regardless of whether the sources are sectarian militias, terrorists, foreign fighters or criminals."
More than 3,000 US troops have died in Iraq
since the US-led invasion in March 2003 [AFP]
On the other hand, Riyad Kahwaji, a Dubai-based defence analyst, told Al Jazeera that Bush is trying to reverse his policy on Iraq.
"Now, after nearly four years and all those casualties, support for the presence of US troops in Iraq has dwindled," he said on Wednesday.
However, 20,000 US troops were unlikely to make a difference to the country's overall security situation, Kahwaji said.
"The level of insurgency is higher than before and so is the possibility of civil war, and if Bush's obvious objective is to control Baghdad, then 20,000 extra troops might be enough to clean up Baghdad of militia men.
"But they will need better luck with the rest of Iraq."
The cost of the new troop increase would be around $5.6bn.
An additional $1.2bn would finance Iraqi rebuilding and jobs programmes.