Moments after House Speaker John Boehner's announcement, President Barack Obama issued a statement congratulating Congress for ending its "partisan stalemate."
The decision to accept the measure came swiftly after the top Republican in the Senate, Minority Leader Mitch McConnell of Kentucky, urged the House to accept it.
The plan, backed by the president, extends a 2-percent payroll tax cut and buys time for working out a full-year renewal.
The House had rejected the measure on Tuesday to kick it back to the Senate, but Senate members had already left Washington for the holidays. Obama told House Republicans that the short-term measure was the only option.
Boehner had insisted on a full-year extension of the existing payroll tax cut before Jan. 1, urging Obama to haul Senate Democrats back to town to talk to his chosen negotiators.
If a deal was not worked out by the end of the year, taxes would have gone up for 160 million Americans on New Year's Day and almost 2 million people would have lost unemployment benefits as well.
The Associated Press contributed to this report.