Like Local 22, AFSCME District Councils 33 and 47, which represent the city's blue- and white-collar workers, have not had a new contract since 2009.
Nutter, who has been targeted by unions citywide with increasingly rancorous protests in recent years, said his decisions have been governed by whether the city could afford to pay a given contract.
The last five years have been particularly lean, with the city's finances struggling to recover from the recession.
Local 22 and the administration first went to arbitration after the union's contract expired in 2009. The first award was issued in 2010. The administration appealed to the courts, calling the award unaffordable.
The dispute was returned to arbitrators, who ruled again in 2012. The administration appealed that award as well.
That appeal had been slated to be heard Thursday in Commonwealth Court in Harrisburg, on the anniversary of the Sept. 11, 2001, terrorist attacks. Firefighters from across the state were expected to pack the courtroom.
Nutter agreed Friday to drop the appeal, saying the improving economy meant the city now could afford to pay.
"The reason for the appeals and the reason for today's decision are consistent," he said. "We could not afford those awards at that time. We now can."
The arbitration award covers a four-year period from 2009 to June 30 of this year. The two sides have begun meeting with arbitrators on the next four-year contract, to run through June 2017.
Richard G. Poulson, an attorney for Local 22, was preparing for next week's hearing when Nutter announced he was dropping the appeal.
Poulson said he would have argued that the city clearly could afford to pay.
"They made the right decision," he said. "It's a shame that firefighters and paramedics and their families have had to work with this issue over their heads for the past four years."
Local 22 president Joseph D. Schulle, elected in May after campaigning that he would end the stalemate with Nutter, said Friday: "This day has been a long time coming."
The administration already had budgeted $112 million in the city's five-year financial plan to give the firefighters their pay increases.
Last month, a Common Pleas Court judge ordered the administration to pay a lump sum into Local 22's health-care fund and to increase the city's monthly contributions.
That order will cost the city $70 million over five years, Nutter said Friday, but the administration did not appeal.
That left a $28 million back payment into the health-care fund as the only outstanding item to resolve the contract. That amount now will be paid as well. Nutter also noted that the award required Local 22 to increase medical and prescription co-pays for its members.
Councilman James F. Kenney intends to introduce legislation this fall that will require future mayors to ask for Council's permission before appealing an arbitration award.
"The city's first responders," Schulle said, "should never again have to wait four long years for economic fairness."
Contact Troy Graham at 215-854-2730 or firstname.lastname@example.org, or follow on Twitter @troyjgraham.