In an adjustment to a worsening economic climate, a triangular parking lot in downtown Brooklyn that originally was slated to be an Enrique Norten-designed public library will be developed instead by Two Trees Management as a mixed-use facility.

The city is expected to finalize the plan in the coming days. In addition to 180 housing units and 187,000 square feet of commercial space, the proposed 371,000-square-foot facility, to be designed by Mr. Norten, will include studios, offices, and performance space for Brooklyn-based arts organizations. The building could also include a small branch library — one much more modest than originally planned.

Under the deal, Two Trees would pay the city $20 million in cash for the site. The developer would also transfer another nearby property, valued at $6.5 million, to the Brooklyn Academy of Music, which would use it to build administrative offices and a new, 263-seat community and educational theater.

The lot to be developed by Two Trees is the southernmost site included in the BAM Cultural District, a $650 million joint initiative between the city and a nonprofit local development corporation called the Downtown Brooklyn Partnership. The cultural district will also include a home for Theatre for a New Audience, designed by Frank Gehry and Hugh Hardy, and a mixed-use tower with studios and performance space for Danspace Project.

The fate of the so-called south site, at the corner of Ashland Place and Flatbush Avenue, had been up in the air since last year, when the city acknowledged that the library plan was no longer feasible because the Brooklyn Public Library had been unable to raise the necessary funds.

Owned by the father and son partners David and Jed Walentas, Two Trees Management is best known as the driving force behind the development of DUMBO. Although real estate values have skyrocketed there, Two Trees still offers free or subsidized space to arts groups, including St. Ann’s Warehouse, Triangle Arts Association, and Galapagos Art Space. In a statement, Jed Walentas described the site for the Enrique Norten building as sitting “at the nexus of Downtown Brooklyn’s commercial core, the cultural district, and some of the finest residential neighborhoods anywhere in America.”

Council Member Letitia James said her support for the new plan hinged on the inclusion of space for local arts groups. “A significant number of groups are being displaced in downtown Brooklyn,” she said. “I demanded that, if any developer wanted my support, they had to include a place for groups that had been in Fort Greene during the bad times and who want to be there during the good times.”

If the city finalizes the plan, the facility will house the Museum of Contemporary African Diasporan Arts, Creative Outlet Dance Theatre Brooklyn, Errol Grimes Dance Group, Evidence Dance Company, and Urban Bush Women.

Ms. James said she is hoping that Two Trees also will carve out affordable housing in the facility. Although two of the other sites being developed will include low- and moderate-income housing, she said that was not enough. “I don’t want segregated housing,” she said.

As for the new BAM annex, which will be on Ashland Place, between Lafayette Avenue and Hanson Place, Ms. James is lobbying the president of BAM, Karen Brooks Hopkins, to allow schools and local arts groups to use the theater at a nominal cost.

The president of the Downtown Brooklyn Partnership, Joe Chan, described the new arrangement as a serendipitous solution to the stalled library plan. “We are enthusiastic that this project will bring an architecturally iconic building to one of the most visible locations in New York City, and that the building will be tenanted by arts and cultural groups that have been cultivated and grown locally,” he said.

The president of Brooklyn, Marty Markowitz, said: “I’m thrilled with these plans for mixed-use spaces, an iconic Enrique Norten-designed building and the demonstrated commitment to community arts and creating affordable housing — which is the best way to preserve the ethnic, cultural, and economic diversity that defines life in the ‘global city’ of Brooklyn.”

In other changes in the development plans, Theatre for a New Audience has agreed to shift its building to a mid-block site from the corner of Lafayette Avenue and Ashland Place in order to allow the Department of Housing Preservation and Development to use the site for affordable housing.

A spokesman for the city’s Economic Development Corporation, Jeff Roberts, said plans for the south site were not yet finalized. “We’re now working to determine what uses will fill the substantial cultural space that will be provided in the development,” he said. “In all likelihood, the ultimate uses will include a combination of various institutions, including ones from the local community.”