His announcement was the latest move in the budget-season chess match in the Capitol between the new Democratic governor and the Republicans who control the House and Senate.
It came a day after House Majority Leader Dave Reed (R., Indiana) said his members would pass and send to the Senate a bill to privatize State Stores by the end of the month - which they say would generate much-needed revenue. Meanwhile, Senate Republicans are pushing for a government pension system overhaul that would change the benefit structure.
Wolf has not supported either proposal, setting the stage for a clash as the commonwealth looks to close a projected $2.3 billion budget shortfall and revisit its seemingly annual debate about education funding.
"One of two things will happen: Everything will come to screeching deadlock, or it's Let's Make a Deal time," said G. Terry Madonna, a political analyst and pollster at Franklin and Marshall College.
Pennsylvania is the only major gas-producing state that does not impose a so-called severance tax.
Wolf announced the details at Caln Elementary School in Thorndale, the first stop on a statewide tour of public schools to showcase the plan that was a cornerstone of his campaign for governor. A similar stop is planned Thursday in Pottsville.
Under Wolf's proposal, called the Pennsylvania Education Reinvestment Act, the state would enact a 5 percent tax on the value of the gas extracted plus 4.7 cents for every thousand cubic feet of natural gas extraction. The governor's office said it is modeled on a tax on drillers in West Virginia.
Such a tax would replace the "impact fee" structure favored by Wolf's Republican predecessor, Tom Corbett. Those fees on drillers generated about $630 million since the act passed in 2012, most of it going to counties and municipalities where drilling occurs.
Senate Majority Leader Jake Corman (R., Centre) did not close the door on the proposal, but said Republicans wanted to address the pension crisis before looking at new revenue ideas - and also plan to take a closer look at the potential economic impact of the drilling tax.
"If it's a billion dollars, that would be an amazing tax, so, look, we'll hold hearings on all his proposals, including this one, to see what they actually achieve, to see whether it helps or hurts the economy of Pennsylvania," Corman said.
Reed said the proposed 4.7-cent fee for every 1,000 cubic feet of gas would bump the overall proposed tax rate from 5 percent to 7.5 percent, which would be one of the highest in the nation.
The administration disagreed, pointing to an Independent Fiscal Office report that it would be a 5.8 percent effective rate based on the West Virginia model.
In a memo to legislators, Wolf said Pennsylvania ranks 45th in the nation in the percentage of funding the state provides for public education. "This is intolerable," his statement said.
While most of the money would boost the state share of funding to schools like Caln - part of a district that receives only 30 percent of its funding from the state - a percentage would go to the Department of Environmental Protection and developing alternative energy sources.
"We've been asked to do more while we receive less," said Cathy Taschner, superintendent of the Coatesville Area School District, which includes the Caln school.
The Pennsylvania State Education Association, the state's largest teachers' union, and environmental groups applauded the tax, saying drillers ought to pay their fair share, while antitax and industry groups called the proposal a job-killer.
The Marcellus Shale Coalition, which represents drilling companies and other businesses that have benefited from the boom, has warned that a severance tax could cripple the industry's growth as it faces falling gas prices.
"While we look forward to evaluating the policy details outlined by the governor today, it's clear that new energy taxes will discourage capital investment into the commonwealth and make Pennsylvania less competitive," said David Spigelmyer, the coalition's president.
PennFuture, a statewide environmental advocacy group, said the gas tax announcement - coming on the heels of his restoration of the moratorium on new gas leases on state lands - demonstrates Wolf's commitment to the environment.
"Pennsylvania has a history of extractive industries that have harmed the environment and left successive generations to pay for the damage," said John Norbeck, the group's acting president. "Gov. Wolf's actions today clearly show that this pattern will come to a close."