NEW ORLEANS — LaToya Cantrell, a City Council member who first gained a political following as she worked to help her hard-hit neighborhood recover from Hurricane Katrina, won a historic election that made her the first woman mayor of New Orleans.

The Democrat will succeed term-limited fellow Democrat Mitch Landrieu as the city celebrates its 300th anniversary next year.

‘‘Almost 300 years, my friends. And New Orleans, we’re still making history,’’ Cantrell told a cheering crowd in her victory speech.

The leader in most polls before Saturday’s runoff election, she never trailed as votes were counted. Her opponent, former municipal judge Desiree Charbonnet, conceded the race and congratulated Cantrell late Saturday. Later, complete returns showed Cantrell with 60 percent of the vote. The women led a field of 18 candidates in an October general election to win runoff spots.

Landrieu earned credit for accelerating the recovery from Hurricane Katrina in an administration cited for reduced blight, improvements in the celebrated tourism economy, and economic development that included last week’s announcement that a digital services company is bringing 2,000 new jobs to the city.

But Cantrell will face lingering problems. Crime is one. Another is dysfunction at the agency overseeing the city’s drinking water system and storm drainage — a problem that became evident during serious flash flooding in August.