A portion of downtown San Francisco will change dramatically with thousands of housing units, jobs — and even a public swimming pool — under a plan finally approved Tuesday by the Board of Supervisors after eight years of hearings, amendments and negotiations.

The Central SoMa plan will revamp a part of South of Market that runs from near Market Street south to Townsend Street, and from Second Street to Sixth Street. The approved plan proposes 8,800 housing units and will create a projected 31,000 jobs.

After the board unanimously approved the plan, Supervisor Jane Kim — who sponsored the legislation — walked out of the Board of Supervisors chamber and gave a sigh of relief.

“We just got this across the finish line before my term ended,” said Kim, who will be termed out in January. “This is the biggest area plan the city has passed.”

Supervisor Sandra Lee Fewer was the only one to express concern about the Central SoMa plan, as it does not include a public school. But, she said, the Planning Department and the San Francisco Unified School District will hold a meeting later this month to determine how to create enough public schools to accommodate the growing population.

“Although this is very difficult for me to vote for a plan that is lacking in a very big way, I want to recognize all the work that Supervisor Kim has put into this and all of the other neighborhood groups that have come out,” she said. “I will be voting in favor, but I just want to note that we as a city have a responsibility to grow families here.”

The rezoning of Central SoMa was initially about creating the large-floor-plate office buildings coveted by tech companies. It originally envisioned about 7,000 housing units and space for about 39,000 jobs. But as the city’s housing crisis worsened over the years, city planners and supervisors pushed to increase the amount of housing.

Under the final proposal, more than 30 percent of the housing units will be affordable. Future board members could also increase the amount of housing and affordable units in the project.

Matt Haney, the candidate expected to succeed Kim after last week’s election results are finalized, said during the campaign that he would push for as much affordable housing units in new developments as possible.

Several appellants came out against the plan over the years, calling for more child care and recreation facilities, more measures to hold off gentrification in the area, shorter buildings and less density. Others wanted taller buildings and more density. All in all, Kim said the Central SoMa plan has been amended more than 100 times.

Josh Switzky, who heads up community planning for the Planning Department, said he was both “elated and relieved” that it was finally approved.

“The hearing was a sedate affair. It masked a lot of the intense passion and discussion about how to best create a sustainable neighborhood,” he said of the board meeting. “This is one of the most complex plans I’ve worked on.”

The plan will get a final vote at the board’s next meeting.

The supervisors also unanimously passed legislation Tuesday introduced by Mayor London Breed to protect 2,298 units of housing — including 340 units of affordable housing — that were at risk because of a 30-month permitting deadline that would have been difficult to meet under the city’s long entitlement process.

These projects were faced with the deadline after San Francisco changed its affordable-housing requirements in 2016. A number of the projects were grandfathered in to keep them moving through the approval process — but the mayor’s office said the 30-month deadline imposed on them to get the permits was “unrealistic.”

The legislation will extend the deadline for projects to secure building permits by 18 months.

“In order for families and working people to be able to afford to live in San Francisco, we need to build more housing,” Breed said in a statement. “This legislation will prevent the loss of thousands of new homes as we work to speed up the approval process for new housing.”

Trisha Thadani is a San Francisco Chronicle staff writer. Email: tthadani@sfchronicle.com Twitter: @TrishaThadani