"We need to move on," he said.
The announcement ended, for now, a historic showdown between the first-term Democratic governor and the GOP-led legislature, one that forced schools and local governments to borrow millions.
"We are happy to be moving forward," said Senate Majority Leader Jake Corman (R., Centre), adding that Republicans would resume budget talks with the governor.
But how and when those differences may be resolved remained as unclear as ever. Corman's counterpart, Sen. President Pro Tempore Joe Scarnati (R., Jefferson), took aim at Wolf in a statement, arguing that the governor "finally ended the crisis he created."
The spending plan to be enacted boosts education funding by $200 million - about half the increase Wolf wanted. It included none of the new or increased taxes he sought to permanently plug what he says is a recurring structural budget deficit of more than $1 billion. Also missing is any action on Republicans' policy priorities: changes to the state's pension and wine and liquor sales systems.
Wolf also added a twist to his decision. He said he does plan to veto the proposed Fiscal Code, the element of the budget that dictates exactly how state revenue is to be spent.
The governor believes the code, as written and approved by GOP lawmakers, would unfairly limit funding for predominantly poorer school districts, improperly alter environmental regulations, and limit certain executive branch powers.
It was unclear whether the legislature would seek to override or otherwise fight that veto.
The governor's decision to relent on the overall $30 billion plan followed a rising chorus of concern from fellow Democrats about the impact of the continued gridlock. Pennsylvania was one of only two states nationwide - the other is Illinois - that failed to pass an annual operating budget last year.
In December, Wolf approved about six months' worth of funding - enough for schools and agencies to keep operating - but vetoed about $9 billion more.
Negotiations since then have been slow or nonexistent. But with coffers again running low, the governor's latest threatened veto intensified fears of school closures and layoffs. That stirred talk in the Capitol that a few Democrats might be willing to break ranks and give Republicans the votes to override a veto.
Wolf insisted Wednesday that that had no bearing on his decision to reverse course. "I've convinced myself that this is the right thing to do," he said.
Democratic leaders echoed that sentiment.
"Harrisburg is broken, and because of that Pennsylvania faces a budget emergency," said Sen. Frank Dermody of Allegheny County. "The governor is taking steps to buy us all some time."
G. Terry Madonna, director of the Center for Politics and Public Affairs at Franklin and Marshall College, said he believed it marked the first time a Pennsylvania governor had taken such an action - or inaction - in " letting a budget become law."
Madonna cited the recent pressure from Democrats and school and human services officials, but said there was an apparent political element to the maneuver, too.
By neither signing nor vetoing the bill, he said, Wolf leaves none of his "fingerprints" on the plan. At the same time, he conveys a message: "This is your budget, Republicans in the legislature. You're responsible for it."
Sen. Vincent Hughes of Philadelphia, the ranking Democrat on the Appropriations Committee, said he knew this was an option Wolf was considering in recent days.
Hughes said it was difficult to ignore the advocacy from school districts, who rattled Republican and Democratic cages in the Capitol after Wolf threatened his veto.
"They were much more publicly engaged than they have ever been," Hughes said. "I think that activated more Republican and Democratic legislators than I think the entire previous 81/2 months had."
Guido M. Pichini, head of the State System of Higher Education Board of Governors, said he welcomed what he called the first appropriation increase in seven years. But public-school officials found the agreement wanting.
It failed to address the need for a more-equitable funding formulas, said Nathan Mains, head of the Pennsylvania School Boards Association.
"This budget does not address the serious long-term fiscal challenges that face Pennsylvania's school districts," said Jim Buckheit, executive director of the Pennsylvania Association of School Administrators.
"This isn't the kind of budget that our schools need or that our students deserve," said Jerry Oeksiak, a special-education teacher in the Upper Merion Area School District and head of the Pennsylvania State Education Association, the largest teachers union.
"I'm glad to see that we finally have a budget," said Joseph Ciresi, who has made several trips to Harrisburg to protest the stalemate. "I still think we have to work on fair funding and a better formula. Are we going to get in the same battle next year? We're only three months away until we get the next budget."
Contributing to this article were staff writers Susan Snyder, Anthony R. Wood, and Martha Woodall.