The Democratic-controlled Senate's bipartisan compromise won approval by 81 votes to 18.
The deal was then passed by 285-144 in the House of Representatives, whose Republican leadership begrudgingly agreed to support the measure.
It came hours before the deadline to raise the $16.7tn (£10.5tn) limit.
The bill yanked the US back from the brink of a budgetary abyss by extending the treasury's borrowing authority until 7 February.
It also funds the government to 15 January, reopening closed federal agencies and bringing hundreds of thousands of furloughed employees back to work.
President Barack Obama signed the bill into law early on Thursday morning.
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