The House is expected to vote on the legislation shortly.
The government will be funded through Jan. 15 at current spending levels, as established by the automatic budget cuts known as sequestration.
The debt limit will be raised through Feb. 7, and the Treasury can use extraordinary measures to borrow money after that date, if necessary.
A bipartisan House-Senate conference committee will convened and charged with submitting formal budget recommendations by Dec. 13. Prior to the vote, the Senate agreed by unanimous consent to go to conference. Sen. Patty Murray, chairwoman of the Senate Budget Committee, made the motion, which had previously been blocked 21 times.
The administration will be required to verify that people seeking subsidies to buy insurance under Obamacare have an income level makes them eligible for assistance under the law.
Workers furloughed during the shutdown will also receive back pay.