The city joined forces with the owner of the New Jersey Nets, Bruce Ratner, to announce a deal yesterday that would bring more than 2,000 units of “affordable housing” to Brooklyn as part of the proposed Atlantic Yards development plan.

Mr. Ratner, who hopes to build an arena nearby for his professional basketball team, agreed to set aside half of the development’s 4,500 new rental units for low- and middle-income families, and, for the first time, expanded upon the details of the plan.

Under the agreement, 20% of the affordable housing will be reserved for low-income families of four making less than $31,400, and 30% of the units will be set aside for middle-income families of four with incomes of up to $100,000. Half of the affordable-housing units are to be reserved for Brooklyn residents. The rest of the units will rent at market value.

Mr. Ratner, president and CEO of Forest City Ratner, the development firm, announced last fall his intentions to build affordable-housing units as part of the plan for the Atlantic Yards, but until yesterday, he had yet to put those plans in writing.

Fearing the new development would consist only of luxury condos, community officials urged the developer to sign a community-benefits agreement, promising to provide affordable units and jobs for the neighborhood.

“We are fortunate that our elected officials are paying attention to this housing crisis,” the executive director of ACORN, Bertha Lewis, said. “This is a giant step in the right direction for New Yorkers of all income levels.” The acronym stands for Association of Community Organizations for Reform Now.

Even opponents of Mr. Ratner’s $2.5 billion proposal to build a 19,000-seat basketball arena over the rail yards near Atlantic and Flatbush avenues said the agreement was a victory for Brooklyn’s low-income families.

“Congratulations to all parties for putting this deal together,” the neighborhood’s City Council member, Letitia James, said. Ms. James, a Democrat, has opposed the arena proposal since its unveiling in December 2003.

“I am glad that they recognize that affordable housing is a priority in our district,” she said yesterday.

Ms. James was less enthusiastic about the overall plan, saying Forest City Ratner has failed to address key issues regarding traffic, scale, and economic benefits to the surrounding community.

“It just seems that they are trying to sweeten the pot,” she said.

City housing agencies have agreed to finance a portion of the construction costs for each unit of affordable housing through tax-exempt bonds and housing subsidies, although a total amount has not been determined yet, a spokeswoman from the Department of Housing Preservation and Development, Carol Abrams, said.

Financial assistance from the city comes as part of a wider initiative under the Bloomberg administration to increase affordable housing in New York.

Ms. Abrams said the money for the affordable housing would come in addition to the $100 million in capital contributions already pledged by the city and state for infrastructure improvements in and around the Atlantic Yards site.

Mr. Ratner’s plan covers 21 acres, including the defunct rail yards and spilling over onto surrounding streets in Prospect Heights. He hopes to develop the property through a combination of private purchase and eminent domain. In addition to the arena, the project calls for 2 million square feet of office space and 4.5 million square feet of residential development, shops, and parking.

The Metropolitan Transportation Authority, which owns the part of the site Mr. Ratner wants to develop, has not decided whether it will sell the rights to develop the site.

Although Forest City Ratner has said the arena will provide thousands of jobs to the community, the proposal has stirred considerable opposition from residents and officials, who said it will displace hundreds of people through an illegal use of eminent domain.

Develop Don’t Destroy is one community group that has aggressively protested the new development. A group spokesman, Daniel Goldstein, said he was pleased with the housing agreement but questioned the public financing of both the affordable rental units and the arena.

“A small bone of ‘affordable’ housing thrown to Brooklynites is far from enough to make Ratner’s plan acceptable,” he said. “Ratner is demanding that the public waste its money on the most expensive sports arena ever proposed, huge skyscrapers in a low-rise community. …” He also predicted serious traffic problems and environmental hazards, should the development go forward.