A bipartisan deal in the Senate cleared a path to undo a scheduled cut to military pensions, as both parties agreed to drop their proposals and accept a House version.

The Senate on Wednesday overwhelming approved a House-passed measure that pays to restore the veterans' benefits by extending for an additional year a 10-year "sequestration" cut to Medicare reimbursements to doctors and hospitals.

The measure, which the Senate passed by a vote of 95-3, now goes to the White House for President Obama's signature.

"I applaud my colleagues in Congress today for doing the right thing," said Sen. Jim Inhofe of Oklahoma, the senior Republican on the Senate Armed Services Committee. "Our men and women in uniform deserve the best, and I applaud my colleagues for keeping politics out of this vote."

There had been wide bipartisan support to undo the cost-of-living-adjustment pension cut since it was included in a December budget agreement brokered by Rep. Paul Ryan, R-Wis., and Sen. Patty Murray, D-Wash. -- a move that caught many on Capitol Hill off guard.

But each party and chamber took different approaches to resolving the issue. Democrats wanted a "clean" bill that would undo the cuts without paying for them, while separate House and Senate Republican proposals called for the costs to be offset.

The sides appeared to be at a standoff earlier in the week. But after the House on Tuesday easily approved their version by a vote of 326-90, Senate leaders — eager to avoid a lengthy debate that would've played badly with the nation's veterans — decided it was more politically prudent to take up the House bill and move on.

Senate Majority Leader Harry Reid, D-Nev., said his chamber deserves credit for jump-starting the measure, arguing that a 94-0 procedural vote in the Senate Monday that advanced a Democratic version of the bill "forced the House to act fast" a day later.

"It is encouraging that some of my Republicans colleagues seem to be regaining their grip on sanity this week," said Reid on the Senate floor.

Under the December budget deal — which keeps the government funded through September 2015 — annual cost-of-living increases for veterans age 62 and younger would have been held to 1 percentage-point below the rate of inflation.

The change, which was to begin in 2015, would've cost a sergeant first class who retired at 42 after two decades of service an estimated $72,000 in reduced pension payments, the Associated Press reported.

Military groups, while praising Congress for its action, noted the legislation doesn't remove the pension penalty on future retirees who enter the military after Jan. 1.

"The world will remain a very dangerous and unpredictable place even after America ends its involvement in Afghanistan, and future military retirees will be required to serve just as long and perhaps sacrifice even more than their predecessors," said William A. Thien, commander-in-chief of the Veterans of Foreign Wars.

American Legion National Commander Daniel M. Dellinger said his group "will continue to push toward a full repeal of military pensioners’ [benefits] cuts."