San Francisco Board of Supervisors president London Breed (D) will become the first black woman to run the city on a permanent basis after her chief rival in last week's election conceded defeat Wednesday .

Breed, 43, won more first-place votes than any other candidate running in the June 5 primary, though San Francisco's ranked-choice voting system meant election officials had to reallocate second- and third-place votes from other candidates who were eliminated round by round.

Tuesday's election was the first time San Francisco voters elected a new mayor using the ranked-choice format.

Her second-place rival, former state Sen. Mark Leno (D), called Breed on Wednesday morning to concede defeat. With a few thousand ballots left to be counted, Breed led Leno by a margin of less than one percentage point, fewer than 2,000 votes.

At a press conference Wednesday , Leno said he had been beaten by "a remarkable young woman."

Breed became the first black woman to head the city in December, when she temporarily filled the post left vacant by the death of her predecessor, Ed Lee. Her election last week means she will fill the remainder of Lee's term, which runs through 2020.

Breed is a native of San Francisco who was raised by her grandmother in the city's housing projects. Her family relied on government handouts, and she has written that her community experienced endemic violence when she was a child. One of her sisters died of a drug overdose

"I am from the 'hood," she told a San Francisco Chronicle columnist in 2012 , when she won her supervisor's seat in an upset over several more liberal candidates. "I spent more than half my life in what was considered the worst public housing in the city. Taxis wouldn't come there. People wouldn't come to my house. I saw my first homicide when I was 12."

She has made the region's growing housing crisis a focal point; the median single-family home in San Francisco is selling for more than $1.6 million, making it the hottest real estate market in the country, at a steep cost to the city's middle class and low-income residents.

She got her start in city government as an intern in a housing and neighborhood services office in Brown's administration. Then-Mayor Gavin Newsom, now the leading candidate to become California's next governor, appointed her to serve as a city fire commissioner, before she won her seat on the county board of supervisors.

"I just think that my perspective is different than some of the other people who have tried to change it from the outside. I'm coming from an insider's perspective of someone who spent more than half their life in arguably the worst public housing developments during that time," Breed told a neighborhood newspaper when she took over her supervisor's seat.

On the board of supervisors, she spearheaded the strictest ban on Styrofoam food containers in the country, and she authored legislation allowing the city attorney to seek civil damages from those caught spraying graffiti, rather than criminal charges.

She had been widely expected to run for mayor when Lee's second term expired in 2020.

Breed is the latest in an unprecedented run of black women who have won election in recent years to run some of the nation's largest cities. The mayors of Atlanta, Baltimore, Charlotte, New Orleans and Washington, D.C., are all black women.