The number of people sleeping in New York City homeless shelters has risen to nearly 60,000, according to an official city count released Thursday, reviving questions about the effectiveness of Mayor Bill de Blasio’s policies to combat homelessness.

Since Mr. de Blasio took office on New Year’s Day in 2014, when the homeless count was 50,689, the number of people in city shelters has grown 18%. During his campaign for mayor, Mr. de Blasio, a Democrat, vowed to make homelessness a priority of his administration.

Administration...