A huge shopping center in the South Bronx cleared its last major hurdle yesterday.

The City Council overwhelmingly approved the Related Companies’ application to build a million square feet of retail space at the site of the Bronx Terminal Market. Demolition on the existing buildings, just south of Yankee Stadium, could begin as early as June, the developer said.

The nearly unanimous council vote did not reflect the layers of difficulties that have surrounded the project. Union leaders worried that a big-box store with poor labor practices, like Wal-Mart, would end up occupying the mall. Neighborhood advocates said the mall’s stores would exclude the area’s residents, among the poorest in the city, and that the added competition would hurt local businesses.

Some local leaders also expressed concern for the future of a group of ethnic food purveyors who occupy the Bronx Terminal Market. And government watchdogs charged that the developer’s no-bid lease for the site was too laden with incentives and was born from a close relationship between the developer and City Hall.

In a statement yesterday, Mayor Bloomberg hailed the project as a victory for the residents of the South Bronx, saying: “The project will keep shopping dollars in the Bronx that are flowing to New Jersey and Westchester, and create new open space along the Harlem River.”

Yesterday’s approval coincided with the signing of a community benefits agreement between the Bronx delegation of council members, the president of the Bronx, Adolfo Carrion, the project developer, the Related Companies, and members of some neighborhood groups. It aimed to address some of the contentious issues.

Council Member Joel Rivera, a Democrat of the Bronx, said a community task force assembled to negotiate the agreement initially sought $30 million from the developer. An attorney for Related, Jesse Masyr, said the final agreement cost the developer about $5 million.

The agreement specifically banned the presence of Wal-Mart or a Wal-Mart subsidiary in the mall. It also said that Related would pay $3 million to a job-referral program that aims to help employ local Bronx residents. It also set certain thresholds for construction dollars and retail space to award to local businesses. Should a store that charges a membership fee locate at the mall, like BJ’s Wholesale Club, the developer will pay half the membership fees for 2,000 local families. Annual membership fees at BJ’s are about $45.

Yesterday, council members of the Bronx and Mr. Carrion touted the agreement as one of the biggest and most valuable community benefit agreements ever signed.

“We got more concessions than mostly any other CBA in the United States of America,” Mr. Rivera said. “It is never perfect, but it is pretty darn close to it.”

Yesterday, the representative of the Bronx Terminal Market merchants who have been fighting their eviction and the amount of their initial $8 million relocation package, Stan Meyer, said a deal with the city to secure about $2 million more in relocation funds was close to being signed.