The Republicans who lead Arizona’s largest county agreed this week on a plan to administer its elections, ending a yearlong power struggle that threatened to upend the democratic system in one of the nation’s fiercest political battlegrounds.

Elections duties in Arizona are by law split between a county’s board of supervisors and its recorder, but in Maricopa County — home to Phoenix — the two sides have been debating over the specifics.

The recorder, an ally of President Trump who has refused to say whether the 2020 and 2022 elections were fair, sued the Republican-led board last year, claiming the supervisors had illegally seized some election responsibilities, funding and information technology systems that were rightfully his. The board fought the suit and said the recorder, Justin Heap, wanted to sow chaos and doubt in the county’s elections.

The legal settlement, reached after hourslong late-night negotiations and approved at an emergency board meeting on Tuesday, follows months of recriminations, invective and intervention from the State Supreme Court.

The agreement details which party is responsible for which functions, with the board generally overseeing Election Day voting and tabulation, while Mr. Heap’s office remains in charge of voter registration and early voting. The board also earmarked up to $15 million to pay for the recorder’s new I.T. system and committed to funding dozens of new staff positions.

“This settlement agreement now provides an off-ramp from this highway to hell that we’ve been on,” Tom Galvin, one of the board’s four Republican supervisors, said at the meeting. “It’s not perfect, but overall it provides certainty for how we move forward in running elections.”

In a statement, Mr. Heap said the settlement would “establish a clear framework for administering elections moving forward.”

“Today’s agreement concludes the current litigation, but its success will ultimately be measured by its faithful implementation,” Mr. Heap said. “My office is ready to carry out every responsibility entrusted to us under Arizona law, and we remain committed to delivering elections that are lawful, secure, transparent and worthy of the public’s trust.”

Mr. Heap agreed to the settlement just days after the State Supreme Court delivered him a key victory, ordering the enactment of an interim plan he proposed that would govern the primary elections, which are already underway. The settlement preserves Mr. Heap’s plan for the primary and will officially kick in ahead of the general election, which will determine control of the state’s top offices and, perhaps, Congress.

Mr. Heap’s lawyer, James Rogers of America First Legal, the firm founded by the White House deputy chief of staff Stephen Miller, called the pact “a massive victory for Maricopa County and Arizona elections as a whole.”

Some fear the fight is not yet over. Steve Gallardo, the board’s only Democrat and the lone supervisor to vote against the settlement, said he does not trust Mr. Heap to administer a fair or drama-free election.

“This is not the last of it,” Mr. Gallardo said at the emergency meeting on Tuesday.

The settlement also does not resolve a separate dispute between America First Legal and the elected county attorney, Rachel Mitchell, a Republican who has opposed the firm’s involvement in the case and has accused it of “an unprecedented power grab.”

Both Mr. Heap and the board of supervisors had warned that their long-running legal feud threatened to undermine voter confidence in a county with a turbulent recent history of election-related controversy.

Maricopa has been a cauldron of conspiracy theories since Joseph R. Biden Jr. won Arizona in 2020 and Mr. Trump falsely claimed fraud in the county had led to his defeat. In 2022, Kari Lake also sought to overturn her loss in the Arizona governor’s contest. After those elections, armed protesters surrounded county buildings, and elections officials who rejected the bogus claims were battered by death threats and political challenges.

Kate Brophy McGee, the Republican who chairs the board of supervisors, said she hoped the settlement would be the beginning of a new era of “elections that nobody worries about, has anxiety attacks about.”

“This agreement lets us do what I have wanted to do since I took office,” she said. “Make Maricopa County boring again.”

Nick Corasaniti contributed reporting.