It is only the third time in 50 years that the Republicans have simultaneously held both the Congress and the presidency.
"
My passion lies in the Senate
"
Tom Daschle
The session is expected to be dominated by rival Republican and Democratic party plans for boosting the economy, and potential confrontations with Iraq and North Korea.
But the Senate's session began with a show of unity, as the two parties united to push through a bill providing extra unemployment benefits for around 750,000 jobless.
Meanwhile, Senate Democrat leader Tom Daschle announced that he did not intend to stand for the presidency in 2004.
As Congress convened, President George W Bush put forward a $674bn economic stimulus plan.
It included tax breaks for stock market investors which have been denounced by the Democrats.
Momentum lost
The Republicans only hold slender majorities in both the House of Representatives and the Senate.
In the House, the balance is 229-205, but in the Senate a mere two seats separate the parties.
A BBC correspondent in Washington says that the Republicans have lost some of the momentum they gained in winning back the Congress, because of the recent resignation of their former leader in the Senate, Trent Lott.
Mr Lott was forced to resign, after making comments which appeared to support policies of racial segregation, and has been replaced by Tennessee Senator Bill Frist.
Republican Dennis Hastert has been sworn in for a third term as House Speaker.
San Francisco Democrat Nancy Pelosi was sworn in as the House Minority Leader, the first woman to lead a party caucus in Congress.
"We need to govern in new ways beyond the simplistic labels of left and right," she said.
Pulling out
Mr Daschle started the new Congress by announcing that he would not be seeking his party's presidential nomination in 2003.
"My passion lies in the Senate," he said, surprising many who had believed he would challenge George W Bush for the presidency.
His decision gives a boost to former House Democratic leader Richard Gephardt, who will have a clearer shot at the nomination without Mr Daschle's candidacy.