The package would mark the biggest tax cuts since the 1980s. The bill was passed by 51 votes to 49, after a series of amendments in a marathon session.
Democrats complained the bill only benefited the wealthy and big business.
The plan sees a sharp cut in corporation tax, but a Senate committee finding has warned it would add $1trillion to the budget deficit.
Donald Trump wants the measures enacted by the end of the year and congratulated Republicans for taking the US “one step closer to delivering massive tax cuts for working families”.
The Senate will now have to merge its legislation with that passed last month by the House of Representatives, before it can be signed into law by the president.
Presiding over the Senate, VP Mike Pence declared the 51-49 victory to applause from Republicans in the early hours of December 2.
The new tax plan would see the corporate tax rate lowered from 35% to 20%, and include more modest tax cuts for individuals across income levels.
Following the vote, Senate Democratic leader Chuck Schumer said his opponents would pay the price at the ballot box in mid-term elections next year.
He said the measures would endanger social security and medical provision.
Republican Senate majority leader Mitch McConnell said the legislation would prove to be “just what the country needs to get growing again”.
The final draft of the Tax Cuts and Jobs Act bill went through several changes on December 1 in order to bring reluctant Republicans on board. Republicans have a 52-48 majority in the Senate.
Democrats were angry about the last-minute revisions, complaining that they had not been given enough time to digest the nearly 500-page document, with handwritten changes to the legislation.
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