The move comes despite a last minute snag in the House of Representatives, which had earlier passed the legislation before it was found that multiple provisions violated Senate rules.
The bill will have to be passed again by the House, with those measures withdrawn - both chambers of Congress must pass identical bills before the president can sign it into law.
There was no Democratic support for the contentious $1.5-trillion package of tax cuts for businesses and individuals that critics say will particularly benefit the wealthy.
The Democratic Senator Bernie Sanders was quick to criticise the bill's passage through Congress.
"We are witnessing highway robbery in broad daylight," Sanders told reporters in the Senate lobby.
"It is a victory for wealthy Republican campaign contributors who will see huge tax breaks for themselves while driving up the Federal deficit."
The reform is the most comprehensive revamp of the tax code in three decades.
RFI's Philip Crowther in Washington says this is seen as a major victory for Trump and his party. He says 95 percent of Amercicans will get some form of tax cut, adding that the biggest gains will be for the wealthy.
"Trump has been selling his tax reforms as a 'big Chritsmas present' for ordinary Americans. The Republican party has wanted something like this for decades," our correspondent says.