The Board of Supervisors unanimously approved the largest residential complex in the history of the Mission District on Tuesday, 3½ years after the so-called Beast on Bryant was proposed. The OK came despite criticism from some Mission residents that the neighborhood has too many luxury developments already.

But Supervisor David Campos, who represents the Mission District, said the project at 2000-2070 Bryant St. was a good deal that would bring much-needed affordable housing to the neighborhood.

Over the past year, developer Nick Podell took extensive strides to appease opponents, including giving adjacent land to the city for it to build affordable housing.

“I believe that on balance this neighborhood is better off having this project approved than not,” said Campos, who just a year ago supported an 18-month moratorium on the construction of market-rate housing in the Mission.

“If I had it within my power, I would only be approving projects that are 100 percent affordable,” Campos said. “But at some point we have a responsibility not only to prevent bad things from happening. We also have a responsibility to make good things happen in the neighborhood. And as a district supervisor I have a responsibility to make sure that affordable housing is built.”

As approved, the complex will contain one building with 191 market-rate apartments and a second building with between 100 and 136 affordable units. Podell would develop the market-rate units while the city would construct the affordable ones, one-third of which will house formerly homeless families. The city has reserved $30 million to construct those units.

The project had become a flash point in the debate over the city’s housing crisis and the displacement of longtime residents who can no longer afford to live here. Those tensions are especially fraught in the Mission, a neighborhood famous for its arts and working-class Latino community, but where luxury condominiums and new restaurants are replacing rent-controlled apartments and laundromats.

The property at 18th and Bryant had been home to a treasured arts community, a 50,000-square-foot space for hundreds of dancers, painters, actors and circus performers, among others.

“This project is not necessary and desirable,” said Peter Papadopoulos of the Mission Cultural Action Network, who appealed the project on environmental grounds. “This project will result in additional displacement. The influx of wealthier residents that will accompany this project will create pressure on lower-income residents and mom-and-pop businesses.”

Papadopoulos and others argued that the project had gone through an invalid environmental impact review.

They said the review did not adequately consider the impact of increased traffic and congestion in the neighborhood. They also said it failed to consider the impact of 40 market-rate housing developments in the Mission, a number greater than was anticipated in the 2010 Eastern Neighborhoods plan, which rezoned the area.

Campos expressed sympathy for that point of view. “At some point we do want to cap the number of units that are built as a way to protect the character of a neighborhood,” he said.

But Campos said he could not in “good conscience” reject the project on the basis that it violated the California Environmental Quality Act. He said CEQA was not the proper forum to address concerns about displacement.

Critics of the Bryant Street project fear the market-rate building will be constructed years before the city builds the affordable project. The mayor’s office assured Campos at Tuesday’s meeting that it will move immediately to build the affordable units on the donated property. That’s important because the city has received land dedications in the past, but then lacked the funds to get an affordable housing project built.

Kate Hartley, deputy director of the Mayor's Office of Housing and Community Development, said the city would immediately seek bids from developers to build the project. She estimated the developer would take a year to design it, with the permitting process taking another year.

The land Podell is donating has a market value of $22 million. Had his company not given the land or built affordable housing, it would have had to pay the city around $18 million. On Tuesday, representatives for his company said it would give $500,000 to help build a community arts center in the city-constructed building.

It remains to be seen what the approval of the Bryant Street project means for other market-rate Mission District housing projects in the pipeline. They include the “Monster in the Mission” at the 16th Street BART Station, which has been stalled by litigation between the property owner and the developer, and Axis Development’s proposed 117-unit project at 2675 Folsom St.

In August, the Planning Commission approved the 157-unit project Lennar is proposing at 1515 S. Van Ness Ave. after it agreed to rent 25 percent of the units to low- and middle-income families.

Boe Hayward, the spokesman for the Bryant Street project, expressed happiness with Tuesday’s vote.

“It has been quite a ride, but after years of intense community engagement we are proud of this project and appreciate the support of the Board of Supervisors,” he said. “Fundamentally, it is a shame that a Mission project with unprecedented affordability faced such opposition.”

Chronicle staff writer J.K. Dineen contributed to this report.

Emily Green is a San Francisco Chronicle staff writer. Email: egreen@sfchronicle.com

Twitter: @emilytgreen