New York City officials on Thursday said they would sign off on Altice’s $17 billion takeover of Cablevision with several conditions.

The city’s Franchise and Concession Review Committee will vote to approve the deal on May 11, so long as Altice reaches an agreement with New York state regulators. The state is expected to approve the deal as well when it votes on May 20.

Altice’s agreement with the state Public Service Commission is expected to include commitments “to maintain levels of customer facing employees for an appropriate time period,” according to the city’s draft resolution.

Altice also has agreed that the Bronx and Brooklyn will take priority when it comes to infrastructure upgrades, a spokeswoman for Mayor Bill de Blasio’s office told The Post.

The Federal Communications Commission approved the deal earlier this week.

While Altice was always expected to win federal approval, city officials took more persuading after expressing concerns that Cablevision’s post-deal debt load would lead to job cuts and poor customer service.

New York City Public Advocate Letitia James said in February there was an urgent need for the deployment of high-speed internet in Staten Island, Brooklyn, Queens, the Bronx and upper Manhattan. She said Cablevision would be saddled with too much debt to make improvements.

While European telecom giant Altice questioned whether the city even had the legal authority to block the deal, it still engaged in discussions with officials.

The Post reported Tuesday the city was moving closer to approving the deal and would make an announcement this week.

Bethpage, LI-based Cablevision, controlled by the family of CEO James Dolan, has more than 3 million customers in the metro area.

Separately, Cablevision on Thursday reported better-than-expected earnings for the first quarter. Cablevision said it lost 15,000 pay TV subscribers in the latest quarter, compared with 28,000 in the year-ago quarter.

Profit was $94.4 million, or 34 cents a share, up from $44.6 million, or 16 cents, a year earlier. Revenue rose 1.6 percent to $1.64 billion.

Cablevision shares were up 10 cents to $34.56 in afternoon trading.