CUPERTINO — Apple’s (AAPL) proposed new spaceship-shaped headquarters got a super-charged blast-off Tuesday night when the Cupertino City Council voted unanimously to approve the 2.8-million-square-foot behemoth beside Interstate 280, fulfilling a dream of co-founder Steve Jobs, hatching an iconic landmark for Silicon Valley, and promising more congestion in an already traffic-challenged region for decades to come.

“Steve transformed Apple into one of the most innovative companies in the world and we understand the responsibilities that come from carrying his legacy forward with this project,” Apple’s head of real estate and facilities Dan Whisenhunt told the council. “We’ve designed it with the same care and attention to detail as we do with all Apple products.”

A standing-room only crowd packed the chambers in the hour before the meeting, with several hundred Apple employees filling up much of the room, some of them holding bright green posters with one reading “Cupertino for Apple Campus 2.”

With councilmember Rod Sinks recusing himself because his wife works for Apple, Mayor Orrin Mahoney and his three colleagues quickly took up the matter of Apple’s project: a four-story ring of curved glass housing up to 14,200 employees and surrounded by acres of green space.

Much of the session was a rehash of environmental and other impacts posed by the project, with the first hour devoted to traffic consultants talking about the “significant but unavoidable” impacts on neighboring roadways. Apple has already promised to underwrite a number of roadway improvements to alleviate the congestion throughout Cupertino, and vowed to raise from under 30 to 34 the percentage of its employees who will be using public transit or Apple’s shuttle buses to commute to work.

“The project will certainly cause traffic issues,” said Councilmember Mark Santoro shortly before the vote, “but I’m happy to hear Apple’s going to work with us on solving these problems.”

Whisenhunt, Apple’s point person on the project, said the building would be a manifestation of Jobs’ lifelong love of the city. “Right here at this same podium two years ago,” he said, “Steve shared his excitement about this campus and about creating a home where Apple grew up. Cupertino is synonymous with Apple; it’s on every box” of Apple products “and we’re immensely proud of that.”

During a public-comment session, most speakers wholeheartedly supported Apple, not surprising since Cupertino is a veritable company town, with Apple offices spread far and wide.

“As my mom used to say, ‘don’t bite the hand that feeds you,'” longtime resident Carol Baker told the council. “If we don’t honor Apple with this building, they’ll leave. There’s no reason for them to stay here and be loyal to a community that doesn’t support them. But if they left, it would be a disaster for the city.”

Despite a few objections from speakers about the project’s location and traffic it will produce, supporters including Santa Clara County Sheriff Laurie Smith and Valley tech-industry leader Carl Guardino stepped up to lend their support.

The council’s decision represents a major milestone in Apple’s seven-year campaign to build an iconic corporate home just across Interstate 280 from its current headquarters. From the days in 2006 when the company first began buying parcels in the area laced by Tantau Avenue and Homestead and North Wolfe roads where Hewlett-Packard (HPQ) once had a sprawling campus.

In 2011, the world learned about the company’s ambitious plans when an ailing CEO and co-founder Steve Jobs presented the spaceship-shaped building to city councilmembers. Within hours of that cameo, Cupertino officials were raving about the building’s off-beat design, saying its bold size and shape, along with a pedigree gilded by the involvement of world-renowned architect Sir Norman Foster, would put Silicon Valley architecture center-stage for decades to come.

“This is unprecedented in the United States,” the city’s redevelopment and economic development manager Kelly Kline said at the time. “This is truly a legacy building.”

Now that the project has been approved, the council by regulation must meet one more time on Nov. 15 for a final and largely perfunctory vote. The spaceship, for all practical purposes, has now been approved for liftoff.

Apple says it hopes to start demolishing existing buildings on the site by the end of this year.

Contact Patrick May at 408-920-5689 or follow him at Twitter.com/patmaymerc.