Tax cuts were a key election pledge
Mr Bush, who had made the $1.35 trillion package central to his presidential campaign, said it was about time some of the government's surplus was returned to taxpayers.
Opposition Democrats have attacked the cuts as disproportionately benefiting the wealthy.
They were watered down slightly by Congress but the BBC Washington correspondent says there is no denying the scale of President Bush's political victory.
He said such broad tax relief had only happened twice since World War II - President Kennedy's tax cuts in the 1960s and Ronald Reagan's in the 1980s.
Democrats did not share his glee.
"This is a classic case of opportunity lost. It's full of gimmicks," said Senator Joseph Lieberman, Democrat presidential running mate last year.
Compromise deal
Mr Bush had campaigned for cuts totalling $1.6 trillion, but the proposal did not survive weeks of intense debate in Congress.
House and Senate negotiators finally thrashed out a compromise the weekend before last, and the bill was passed in both houses.
The revised measures include across-the-board reductions in higher income tax rates and the creation of a new 10% tax bracket at the bottom of the scale, below the current lowest bracket of 15%.
Because the tax cuts are retroactive to the beginning of 2001, individual taxpayers will receive a refund of up to $300. Single parents will get up to $500, and married couples up to $600.
Correspondents say the scale of the tax cuts was politically unthinkable six months ago, as was the speed with which they were pushed through.
But the victory may be the last for some time.
The defection of Republican Senator Jim Jeffords a fortnight ago, which gave control of the Senate to the Democrats, will make passing legislation much more difficult for the Bush administration.