After years of lobbying from City Council members and school nutrition advocates, New York City will offer free lunch to all public school students regardless of their families’ income — a change the city expects will result in fewer students missing out on lunch.

The new program — called Free School Lunch for All — will take effect in time for the first day of school on Thursday and will mean that an additional 200,000 students are now eligible for free lunch. It marks the end of a rift between Mayor Bill de Blasio and allies on the City Council who have urged him to enact his campaign promise to make lunch free for all students.

Roughly 780,000 students are currently eligible for free or reduced-price lunch because their household income falls below a certain threshold — more than 70 percent of the city’s student population, advocates say. But families must first fill out paperwork and students must overcome the lunchroom stigma attached to free meals, which discourages some from applying. About one-third of eligible students do not participate, according to advocates.

The de Blasio administration has slowly expanded access to free meals: The city began a pilot program offering free lunch to middle school students in 2014, and currently offers free breakfast at every school.

“This is about equity,” schools Chancellor Carmen Fariña said at a press conference Wednesday, where she was joined by city council leaders, union officials, and advocates. “There is a basic level of investment that every New Yorker deserves.”

Before the announcement, the city had already allocated additional funding that would have ensured roughly 75 percent of the city’s students were enrolled at schools that offered free lunch regardless of income, according to Deputy Chancellor Elizabeth Rose, up from 30 percent last school year.

Under the old program, students had to identify themselves as free-lunch recipients, creating a clear distinction in school cafeterias between students who could afford the $1.75 school lunches and those who couldn’t.

Liz Accles, who has long advocated for universal school lunch as executive director of Community Food Advocates, said the new policy would help eliminate that stigma.

“We’re erasing all the terrible history of the school food program — not just in New York City, but nationally — that has divided children by income,” she said. “This is a new day.”

The Obama administration made a significant push to improve school lunches, and some urban districts — including Detroit and Boston — have rolled out free meals regardless of income. But until now, de Blasio has balked at expanding the lunch program to include all students.

The state recently launched a new system for identifying free-lunch eligible students based on their families’ participation in other government programs, such as Medicaid and food stamps. The new system identified more eligible students, which brought more federal money into the city to help fund an expanded lunch program.

Education officials said the higher reimbursements would cover the full cost of the meals themselves, but the city may have to spend more on food workers.

“We will know final costs when we actually see how many kids actually take advantage of this program,” the education department’s Rose said in an interview, noting that roughly 6 percent more students ate lunch in middle school after the city made it universal.

In the past, Chancellor Fariña has said her “major fear” with offering universal free lunch is that certain high-poverty schools might receive less federal Title I money, since the funding levels are based on how many students qualify for subsidized lunch.

Education officials could not say for sure Wednesday whether moving to a universal system would affect any school’s Title I funding. However, they said schools would continue asking families to fill out paperwork stating their income, even though it will no longer be necessary for students to receive free lunch. The free-lunch-for-all pilot program in middle schools did not have a big impact on any school’s Title I funding, they added.

Advocates have been frustrated with the city’s incremental moves toward universal free lunch. Earlier this year, they criticized Fariña for telling principals to give students free lunch if they asked for it — missing the point that students often don’t ask because they feel embarrassed.

“No child should go hungry in our schools,” said Public Advocate Letitia James, who has previously called on the city to expand free lunch. “This has been a long fight.”