Mayor Bill de Blasio has recruited a Giuliani-era jails commissioner to help get the rising number of homeless people off city street.

During a news conference at a chilly Tompkins Square Park in the East Village — a magnet for the city’s homeless population — de Blasio introduced Michael Jacobson a veteran of not only Giuliani’s administration but also those of mayors Edward Koch and David Dinkins.

He’s now charged with overseeing efforts to reach all of the homeless living on the city’s streets and determine how they got there.

Among Jacobson’s responsibilities will be directing a team of about 60 canvassers as they conduct a daily count of homeless people on every block from Canal Street to 145th Street and other locations they frequent, de Blasio said.

“We’re going to be able to track each person’s trajectory,” de Blasio said as Jacobson stood nearby.

Jacobson is director of the City University of New York Institute for State and Local Governance.

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He has served as a probation commissioner and also worked in the city budget office.

Jacobson shrugged off as “politics” past criticism by Rudy Giuliani of de Blasio’s handling of the growing number of homeless since he took office in 2014.

At the Tuesday news conference, two NYPD cops shooed away a homeless man named Jerry Foust who was watching the event.

De Blasio spokeswoman Aja Worthy-Davis later said officers cleared Foust from the park area because he was drinking an open container of alcohol.

“No enforcement action was taken against him,” Worthy-Davis said in an email, “and homeless outreach will follow-up with him to offer supportive services.”

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The number of people living in homeless shelters — which excludes the estimated 3,000 or 4,000 on the street — was about 30,000 when Giuliani left office, rose steadily through Michael Bloomberg’s three terms as mayor and is now near the all-time high of more than 60,000 tallied in December, 2014, according to figures by the nonprofit Coalition for the Homeless.

Last year, de Blasio initially downplayed the homelessness problem as a tabloid-created exaggeration, but later came to acknowledge the situation as a crisis after criticism from his own police commissioner, William Bratton, and Gov. Andrew M. Cuomo.

As the park Tuesday, de Blasio, Jacobson and other officials stood in front of a blue “From Streets to Homes” city banner . Nearby, Chester Cattouse, 72, watched with skepticism.

Cattouse, an out-of-work carpenter who now lives on the street, said he’d been priced out of his one-bedroom apartment about five years ago on nearby East 10th Street.

“That’s what politicians do,” Cattouse said. “They promise things and they can’t deliver.”