The developer of a project to replace the mostly vacant Vallco Mall in Cupertino, less than a mile from Apple’s spaceship campus, won a key approval from the city as it aims to start construction in September.

The Vallco Town Center project, which includes a proposed 2,402 residential units, 400,000 square feet of retail space and 1.81 million square feet of office, qualifies for streamlined approval under SB35, city staff said. The 2017 law shortens approval time to 180 days for projects that contain affordable housing and meet other requirements including using union labor for construction.

Sand Hill Property Co., which has worked to rebuild the site since 2014 amid local opposition, now expects to receive final city approval by September.

“This is an important first step toward a viable future at Vallco,” Reed Moulds, managing director of Sand Hill Property Co., said in a statement. He said the project will “combat our region’s worsening housing crisis and provide the vibrant downtown environment Cupertino has long desired.”

In order to qualify for SB35, half of the housing will be affordable, with 360 units for renters making no more than 50 percent of the area median income and 841 units for renters making up to 80 percent of the area median income.

Some Cupertino residents opposed the project, saying it would worsen traffic, and called for a smaller development. Two competing 2016 ballot measures — one backed by opponents and one by the developer — both failed to pass.

Prominent architect Rafael Viñoly designed the project, which includes a 30-acre rooftop park, a new movie theater, a bowling alley and an ice rink. Sand Hill Property said it reduced the amount of office space in response to community demands and shrank the retail component in response to “real market conditions.”

State Sen. Scott Wiener, D-San Francisco, authored SB35 in response to what he called excessive regulations that block housing production and exacerbate the shortage of homes around the state.

“Projects ... have been stuck for a long time in cities that are not producing enough housing,” he said Monday.

Wiener said the 1,201 affordable units in the Vallco project will greatly benefit low-income residents and the project’s office component will help subsidize the below-market-rate units. “I’m thrilled that this is happening,” he said.

Cities have struggled to fund affordable housing as federal and state subsidies have plunged since the 2008 recession.

An affordable housing project in San Francisco’s Mission District is also seeking to use SB35 for faster approvals. Another housing project in Berkeley sought to use the bill, but the city said earlier this month it doesn’t qualify because the site is a city landmark.

Roland Li is a San Francisco Chronicle staff writer. Email: roland.li@sfchronicle.com Twitter: @rolandlisf