San Francisco (CNN) For the first time, an African-American woman has been elected mayor of the city of San Francisco.

London Breed reached the milestone on Wednesday, when her opponent conceded a tight mayoral race. Breed will serve until 2020, finishing the term of the late Mayor Ed Lee, who died in December at age 65.

At a short news conference, Breed, 43, praised Lee and thanked her supporters, as well as the other candidates, including Mark Leno, a former state senator who conceded the race hours earlier. She struck an optimistic tone about the city's future.

"I am so hopeful about the future of our city, and I am looking forward to serving as your mayor. I am truly humbled and I am truly honored," said Breed, president of the Board of Supervisors.

She also acknowledged the competitive race: "Whether you voted for me or not, as mayor, I will be your mayor too."

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