New Orleans firefighters will get the full $75 million in back pay they have been seeking from the city for decades, paid for largely with a new tax, in exchange for changes that will make their pension plan less generous for new hires.

Those are among the key provisions of a deal reached Thursday night between the city and the firefighters union.

The deal appears to put to rest the two largest lawsuits hanging over the city’s head while addressing at least some of the criticisms leveled by Mayor Mitch Landrieu and others over the way the pension fund is run and the benefits available to firefighters.

It also lifts the threat of action against the city for contempt of court for failing to pay the judgments, which nearly ended up with Landrieu being placed under house arrest last month.

In a Friday news conference, Landrieu said the deal followed a hard-fought negotiation that wrung significant concessions from both sides.

“A great settlement is one where all sides are squealing, and there was a lot of squealing last night,” he said.

In presenting his 2016 budget proposals Thursday, Landrieu had set a deadline of Thursday night for reaching a deal with the firefighters. Otherwise, he said, the city would walk away from months of negotiations and leave the issues to the courts.

The final deal will guarantee money to those owed back pay and guarantee sustainability for the pension fund, he said.

Two unrelated cases are at the heart of the settlement. One deals with back pay owed to firefighters for raises that were required by state law but never paid by the city for 35 years.

The other case deals with the Landrieu administration’s refusal to make required payments into the pension system until changes were made to put it on a more sustainable financial path. Poor investment decisions have nearly bankrupted the fund, though firefighters point out that the administration’s refusal to pay into the fund also has hurt its financial state.

Combined, administration officials have said, those judgments against the city could total about $400 million, though they also have argued the courts cannot force the city to pay up.

The deal will result in firefighters receiving the full $75 million they are owed in back pay and will require it to be paid more quickly than previously proposed by the city. On the other hand, it requires firefighters to give up claims to judicial interest and other payments they have argued should be part of the settlement.

Instead of requiring an actual payment of the money owed into the pension fund, the agreement allows the administration to make up for that with its annual payments, which will be calculated to ensure the money is there for firefighters when they retire. “We have never missed a pension check for our firefighters, and we never will,” Landrieu said.

As he spoke, Landrieu was flanked by city officials and City Council members, legislators, members of his administration, union officials and representatives of the Business Council of New Orleans and the River Region, a group that attempted to broker a deal earlier this year. All were involved in efforts to reach a settlement, officials said.

Under terms of the deal, firefighters who are owed money because the city did not provide state-required raises decades ago will get a $15 million upfront payment by February and another $5 million by February 2017. Then, starting later in 2017, the city will pay $5 million a year for 13 years, with the money to come from a new 2.5-mill property tax, if voters agree.

It is not clear where the money for the upfront payment will come from. The 2016 budget the Landrieu administration proposed on Thursday sets aside $10 million to pay legal judgments — either the firefighters settlement or some of the $35 million in other judgments pending against the city.

Chief Administrative Officer Andy Kopplin said the administration and the council will have to work out the source of the money for the full payment during the budget process that will roll out over the next month.

The plan also calls for changes to the firefighters pension system for new hires that will mean benefits will accrue more slowly and firefighters will not be able to retire until they are within 10 years of the Social Security retirement age. All New Orleans firefighters can now retire at 50.

Another concession won by the administration will essentially do away with a policy that allowed firefighters to retire with a full pension and collect an additional supplemental disability payment of up to $30,000 a year on top of that for 10 years. Under the agreement, a firefighter’s pension will be reduced by the amount he is receiving in those payments. That is similar to how the state firefighters pension system handles such payments.

Those revisions, as well as changes in how the pension fund makes investment decisions, have been sought by the Landrieu administration as ways of putting the system back on track after years of poor investment decisions essentially wiped out its assets.

The changes are expected to save the city about $275 million in pension contributions over the next 30 years, Landrieu said.

Thomas Meager, a firefighter and secretary-treasurer of the pension fund, said the deal is good for firefighters. “The firefighters do believe in a sustainable pension fund,” he said.

The agreement must still clear a series of hurdles before it goes into effect. The firefighters involved in the suits and the courts must both approve the deal. The City Council and state Legislature also will have to sign off on various aspects of the plan, though with both sides in agreement that should not present much of a challenge.

Voters also will have to approve the new tax in April for the proposal to remain on schedule. The tax is projected to generate about $7.5 million a year, with $5 million going directly to the firefighters who are owed back pay and the rest toward the city’s payments to the pension fund.

Both sides have agreed that the deal will stay in place even if the tax fails. In that scenario, the payments will occur over a longer time frame.

The agreement does leave one dispute between the city and firefighters on the table, involving differing interpretations of how state law requires the pension system to calculate benefits. The interpretation used by the pension fund, and supported by the union, allows firefighters to accrue benefits more quickly than that favored by the city.

Representatives of both sides said they will leave that up to the courts to decide.

Both the cases that led to the agreement have dragged on for years — more than three decades in the back-pay case — even though firefighters have consistently won in court. That’s because while the courts can order the city to pay, state law largely prevents them from enforcing those rulings.

Civil District Court Judge Kern Reese put that legal theory to the test last month when he held the city in contempt for failing to reach a deal with the firefighters and ordered Landrieu to be placed under house arrest on weekends. That order, however, was stayed by the state Supreme Court before it went into effect.

Firefighters union President Nick Felton acknowledged the long-running nature of the dispute Friday as he thanked residents for their patience.

“Thank you to the citizens” of New Orleans, Felton said. “For 35 years, the citizens of the city have put up with this constant bickering.”

Follow Jeff Adelson on Twitter, @jadelson.