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Republicans - who hold a 53-47 majority in the Senate - needed the measure to clear the 60-vote minimum threshold.
Democratic Senators Dick Durbin, John Fetterman, Catherine Cortez Masto, Maggie Hassan, Tim Kaine, Jackie Rosen and Jeanne Shaheen broke from the rest of their party to vote in favour of the funding bill.
They were joined by Maine's Angus King, an independent who caucuses with the Democrats, who also voted to reopen the government.
Only one Senate Republican - Kentucky's Rand Paul - voted with the majority of Democrats against it.
The announcement of the bill's passage was made to a largely empty room, but the senators who stayed until the end cheered and applauded.
"We are going to reopen government, we are going to ensure that federal employees... will now receive compensation that they're earned and deserve," Senator Susan Collins, a Republican who played a key role in authoring the bill, said after it passed.
Many government services have been suspended since October, and around 1.4 million federal employees are on unpaid leave or working without pay.