Senate Budget Committee chairman Patty Murray (D-Wash.) and House Budget Committee chairman Paul Ryan (R-Wis.) announced that they have reached a bipartisan agreement to prevent a government shutdown in January. (The Washington Post)

House and Senate negotiators unveiled an $85 billion agreement late Tuesday to fund federal agencies through the fall of 2015, averting another government shutdown and ending the cycle of crisis that has paralyzed Washington for much of the past three years.

In a rare display of bipartisan cooperation, House Budget Committee Chairman Paul Ryan (R-Wis.) stood side by side in the Capitol with Senate Budget Committee Chairman Patty Murray (D-Wash.) to announce the deal, which would cancel half of the sharp spending cuts known as the sequester for the current fiscal year.

“I am very proud to stand here today with Chairman Ryan to say that we have broken through the partisanship and gridlock and reached a bipartisan budget compromise,” Murray said, calling the agreement “an important step in helping to heal some of the wounds here in Congress and show we can do something without another crisis around the corner.”

Ryan called the agreement “a step in the right direction” that protects the Pentagon from fresh cuts set to hit in January while trimming deficits by more than $20 billion over the next decade.

With the deal already under fire from conservatives for weakening the sequester, Ryan argued that the package represents “a clear improvement on the status quo” by replacing one-time cuts to agency budgets with permanent savings from other programs.

In a “divided government” where Democrats control the White House and the Senate, Ryan reminded his critics, “you don’t always get what you want.”

The deal would not deliver a key demand of many Democrats, to extend unemployment insurance for the long-term jobless. While they pledged to keep fighting, senior Democrats acknowledged that checks are likely to be cut off at the end of the month for more than a million people, potentially undercutting the strengthening economic recovery.

But the agreement could provide an offsetting boost to the economy by returning a degree of normalcy to the Washington budget process and restoring confidence in the ability of Republicans and Democrats to work together after years of destabilizing strife.

“This agreement doesn’t include everything I’d like — and I know many Republicans feel the same way. That’s the nature of compromise,” President Obama said in a statement. “But it’s a good sign that Democrats and Republicans in Congress were able to come together and break the cycle of short-sighted, crisis-driven ­decision-making to get this done.”

The deal was struck after weeks of private talks between Murray and Ryan, a political odd couple better known for advancing their parties’ agendas than for forging compromise. It represents an accomplishment and a risk for Ryan, who ran on the GOP presidential ticket in 2012 and still has White House aspirations.

Under the terms of the deal, spending for the Pentagon and other federal agencies would be set at $1.012 trillion for fiscal 2014, midway between the $1.058 trillion sought by Democrats and the $967 billion championed by Republicans. The Pentagon would get a $2 billion increase over last year, while domestic agencies would get a $22 billion bump, clearing space for administration priorities such as fresh investments in education and infrastructure.

For fiscal 2015, spending would increase only slightly, to $1.014 trillion, for a total of $63 billion in sequester replacement.

That cost would be covered through a mix of policies to be implemented over the next decade. They include $12.6 billion in higher security fees for airline passengers, $8 billion in higher premiums for federal insurance for private pensions, $6 billion in reduced payments to student-loan debt collectors and $3 billion saved by not completely refilling the nation’s strategic petroleum reserves.

Another large chunk of savings — $12 billion over the next decade — would come from reduced contributions to federal pensions, split evenly between military retirees and new civilian workers who start after Dec. 31.

For those in the military, the reduction would take the form of lower cost-of-living increases for retirees between the ages of 40 and 62, many of whom take other jobs while collecting their military pensions. New civilian workers, meanwhile, would be required to contribute an additional 1.3 percent to their retirements.

Current federal workers would not be affected, said Rep. Chris Van Hollen (Md.), the lead budget negotiator for House Democrats. The impact on pensions, one of the last major issues to be decided, was hammered out during a weekend of talks between Van Hollen and Murray, who persuaded Ryan to spread the pain to the youngest military retirees.

“The agreement’s not perfect, but it’s better than none at all,” Van Hollen said, adding that it “replaces part of the job-killing sequester without disproportionately hitting middle-class families, including hundreds of thousands of hard-working public servants.”

On top of sequester replacement, the deal calls for an additional $22 billion in deficit reduction by extending a small part of the sequester into 2022 and 2023. That shift would primarily affect Medicare providers, who would face an additional two years of 2 percent across-the-board cuts.

Ryan and Murray were rushing to file legislation by midnight Tuesday to clear the way for a House vote as soon as Thursday, one day before the chamber is set to adjourn for the year. The Senate would vote before leaving town next week.

Ryan and Murray expressed confidence that the package would win favor in their parties, though Democratic reaction was clearly more positive. Conservatives on and off Capitol Hill attacked the deal, with some outside groups such as the influential Heritage Action for America announcing their opposition a full day in advance.

On Tuesday, Koch Industries, the conglomerate owned by the conservative Koch brothers, sent a letter to members of Congress calling the deal “a dangerous retreat from the pledge to ‘live within our means’ ” made when the sequester was adopted in the summer of 2011.

But as House leaders prepared to brief their rank and file in a closed-door meeting early Wednesday, GOP aides dismissed the outcry, noting that many of the most vociferous critics of the package also opposed the legislation that created the sequester.