A decade after former Mayor Michael R. Bloomberg co-opted a line from “Star Trek” to declare composting the “final recycling frontier,” New York City is finally poised to unveil plans to implement what it is calling the nation’s largest composting program.

On Thursday, Mayor Eric Adams will announce that the city will commit to a 20-month timeline to bring composting to all five boroughs.

The announcement will be part of the mayor’s State of the City address on Thursday at the Queens Theater in Flushing Meadows Corona Park.

The program allowing New Yorkers to put biodegradable refuse into brown bins for composting will be voluntary; there are no current plans to make the composting program mandatory, a step that some experts say is key to its success. But in an interview, Jessica Tisch, the commissioner of the Sanitation Department, said that the agency was talking about the possibility of mandating the composting of yard waste.

“This program is going to represent the first time that many New Yorkers have ever had access to curbside composting,” Ms. Tisch said. “Let them get used to it.”

The announcement comes a month after the city paused a popular boroughwide composting program in Queens, a move that sowed distress among the city’s avid band of food recyclers.

The city’s timeline calls for the program to restart in Queens on March 27, expand to Brooklyn on Oct. 2, begin in the Bronx and Staten Island on March 25, 2024, and finally launch in Manhattan on Oct. 7, 2024.

As Mr. Adams enters his second year in office, he has continued to focus on crime, the budgetary challenges of accommodating an influx of migrants from the southern border, and street cleanliness, with an unusual (and unusually personal) focus on rats.

“By launching the largest curbside composting program in the country, we’ll be dealing a blow to New York City’s rats, cleaning up our streets and keeping millions of pounds of kitchen and yard waste out of landfills,” Mayor Adams said in a statement. “By the end of 2024, every New Yorker, all 8.5 million people, will have the solution they’ve been waiting two decades for, and I’m proud my administration was able to get it done.”

The city’s progress toward Mr. de Blasio’s goal has been nominal. Its so-called curbside diversion rate for recyclables now stands at a paltry 17 percent. Seattle, by way of comparison, had a nearly 63 percent diversion rate in 2020, according to the Citizens Budget Commission, a nonpartisan watchdog group.

In an interview on Wednesday, Ms. Tisch acknowledged that the city had not made enough progress since 2015 to “realistically believe that we will reach zero waste by 2030.”

But she also predicted that the new composting program would dramatically increase the amount of waste diverted from landfills — part of the city’s efforts to address climate change. When added to a landfill, yard waste and food scraps produce methane, a gas that traps heat in the atmosphere and warms the planet.

New York City’s composting program has gone through many fits and starts over the years. Today, the city requires many businesses to separate their organic waste, though it is unclear how effectively the city enforces those rules. The city said it does not collect data on how much waste the program diverts from landfills.

The city was also already offering voluntary municipal curbside composting in scattered parts of Brooklyn, the Bronx and Manhattan when Mr. Adams announced in August that it would come to every single residence in Queens that October.

As part of the program in Queens, which paused for the winter in December, collection times coincided with the pickup of recyclables. And residents did not have to individually opt in to the new service. The program cost roughly $2 million, the department said.

Some composters who had successfully altered their habits to accommodate the new program said the December pause was frustrating and, by upending newly established routines, counterproductive.

But city officials quickly labeled it a triumph, saying it outperformed the prior, existing program and was cheaper, too.

“We finally have a mass market sustainability program that will meaningfully move the diversion rate in New York City,” Ms. Tisch said.

The program will cost $22.5 million in the 2026 fiscal year, the first full fiscal year when it will be running citywide, she said. The city will also have to spend $45 million upfront this fiscal year to buy new trucks to collect the compost.

Once collected, the department will transport the compost to anaerobic digesters in Brooklyn and Massachusetts, and a city-run compost facility on Staten Island, among other places.

Citing a potential recession and the drop-off in pandemic-related federal aid, Mr. Adams has been taking steps to reduce costs, including cuts to public libraries that leaders say could force them to reduce hours and programming. The Sanitation Department has been one area where he has shown a willingness to fund new programs.

Sandra Goldmark, director of campus sustainability and climate action at Barnard College, said she was “thrilled” by the mayor’s commitment and hoped that the program would eventually become mandatory for businesses and residences, just like recycling.

Barnard has worked to implement composting, she said, but it requires a “culture shift” to help people understand the benefits.

“It’s actually so much better in your home — there’s no big, giant trash bag with smelly, gnarly stuff,” she said. “You put wet food scraps in a separate container and it makes all of your trash less gross.”