Three of the city’s political party bosses decided yesterday to back Christine Quinn as the next speaker of the City Council, ending months of deadlock and setting the stage for the body to elect its first female and its first openly gay leader.

The development all but guarantees that Ms. Quinn, 39, will beat out Council Member Bill de Blasio, her main rival, and five other candidates in the race to get the 26-vote majority needed to win when the council elects its new leader tomorrow.

Word began to leak out yesterday morning that the Queens Democratic Party had decided to back Ms. Quinn and that party leaders in Brooklyn and the Bronx were also on board.

The job is one of the most powerful in the city because the council has important land-use authorities and control over part of the budget. It also serves as a counterweight to the mayor’s authority.

Ms. Quinn, who until the end of 2005 was chairwoman of the Health Committee, will likely place priority on health and social service issues. She has a mixed record on development, backing a large rezoning of the West Side but coming out against the proposed Jets stadium. She also has introduced legislation that is widely viewed as anti-Wal-Mart, backed the smoking ban, and in general sides with tenants versus landlords.

Mr. de Blasio called Ms. Quinn to concede the race yesterday and issued a public statement early last night making it official.

“I’ve given this race my all, but my colleague, Christine Quinn, has the support to win,” he said in a statement. “Now it’s time to unite the council and ensure a strong Speaker, so I am supporting Chris to be the next Speaker of the City Council.”

A political operative who ran Senator Clinton’s last campaign and headed Senator Edwards’s presidential bid in New York, Mr. de Blasio said he was “grateful” to the those who backed his candidacy, but urged them to “join me in supporting Chris.” He said he is confident she will lead the council in a “progressive direction.”

Despite more than a year of political jockeying, coffee meetings, and donations to fellow members, the race to replace the previous speaker, Gifford Miller, who was termed out of office, seems to have boiled down to county input.

Queens has historically delivered a large bloc of votes and as a result has become the key that opens the gate to the speakership. Political analysts said that if yesterday’s deal is rubberstamped it will solidify the county as a powerful player in a race that is decid ed largely behind closed doors.

“I think it’s clear from this that the county organizations are still powerful and that Queens makes out like a bandit again,” a professor of public affairs at Baruch College, Douglas Muzzio, said.

In exchange for its support, Queens is likely to hold onto the chairmanships of the council’s two most powerful committees, land use and finance. It was unclear yesterday what Brooklyn and the Bronx would get for their support, but the chairmanships of several committees, including education, health, and government operations, are now up for grabs.

Assemblyman Vito Lopez, the new leader of the Brooklyn Democratic Party, told The New York Sun he joined with Queens County to deliver eight votes from his borough for Ms. Quinn.

He said he talked to “some of the Queens people” until after midnight yesterday, but that the county didn’t make its final decision until morning. That, he said, is when he Mr. de Blasio’s supporters began calling to switch allegiances.

Mr. Lopez said that four years ago the Bronx partnered with Queens to “fill the void” and that “Brooklyn was shut out.” This time: “I went with Quinn and helped close down the deal so that Brooklyn was able to participate in the process,” he said.

The chairman of the Bronx Democratic Committee, Jose Rivera, said there has been a “working relationship between Queens and the Bronx for the last four years” and that “it continues to be Queens and the Bronx.”

He was in Nicaragua over the week end, but said “the cell phone works in Central America” and that he was very much involved in the final deal. Several phone calls to leaders in the Queens party were not returned.

There were some de Blasio supporters who seemed disappointed by Mr. Lopez’s decision to go with Ms. Quinn, who represents Manhattan, when there was a viable candidate from Brooklyn. When Mr. Lopez was elected to head the county delegation, many said it would be a blow to Mr. de Blasio’s chances because of their respective political allies.

Council Member Letitia James, who represents Bedford-Stuyvesant, Fort Greene, and other parts of Kings County, called it a “sad day for Brooklyn.”

“I’m disappointed that Brooklyn could not bring home the bacon,” Ms. James said. Last week, Mr. de Blasio reportedly had a group of 15 supporters.

The other council members in the running were Melinda Katz, Leroy Comrie, and David Weprin of Queens; Lewis Fidler of Brooklyn, and Joel Rivera of the Bronx.

With the vote not set to take place until tomorrow, Ms. Quinn chose her words cautiously yesterday. She is expected to hold a news conference today.

“I am gratified for the support of my colleagues,” she said in a statement. “I look forward to the vote on Wednesday and to working with them to improve the lives of all New Yorkers.”

If elected, she will be both the first female leader of the council and its first openly gay leader.

“It’s historically significant for an openly gay elected official to rise to such a powerful city position,” the head of the Citizens Union, Dick Dadey, said.

Mr. Dadey, the former head of the Empire State Pride Agenda, one of the largest gay and lesbian lobby organizations in the state, said it was “emblematic of a coming of the gay and lesbian community in the city.”

Ms. Quinn got into politics in the early 1990s when she worked for then-Council Member Thomas Duane, the first openly gay member of the body. Immediately before getting elected to his seat in 1999, she headed the New York City Gay and Lesbian Anti-Violence Project.

The council’s Republican minority leader, James Oddo, who is close with Ms. Quinn despite their ideological differences, said yesterday he was personally proud of her.

“I have a great deal of respect for her political acumen. She really went out and won this one. She has handled the last year with a great deal of tact. I really thing it’s good thing for the body”

He said a line in the HBO program “Rome” recently crystallized the speaker’s race for him. “Arithmetic has no mercy,” he said. “There will no mercy in the arithmetic for the person who comes in second. Once the dominos start falling nobody wants to be on the wrong side.”