The package would mark the biggest tax overhaul since the 1980s. It was passed by 51 votes to 49, after a series of amendments in a marathon session.
Democrats complained it 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 $1tn (£742bn) to the budget deficit.
President Trump wants the measures enacted by the end of the year and he congratulated Republicans for taking the US “one step closer to delivering massive tax cuts for working families”.
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