File-sharing giant Dropbox has signed the biggest lease in San Francisco history, an agreement for 736,000 square feet, the entirety of a new office complex under construction in the southwest corner of Mission Bay.

On Tuesday the developer, Kilroy Realty Corp., announced that Dropbox will take all the office space at the Exchange on 16th, a $570 million speculative development that represents the last prime office headquarters building site up for grabs in Mission Bay.

The space will represent an expansion for Dropbox, which occupies 182,000 square feet at 333 Brannan St., a building Kilroy also owns, as well as 115,000 square feet at 345 Brannan. Dropbox currently has about 1,500 employees and 102 job openings in San Francisco, according to its website.

The Exchange on 16th, designed by Rios Clementi Hale Studios, is a sprawling concrete structure that reads like four distinct buildings in a mix of glass, brick, timber and other materials. Like a tower set on its side, the building stretches 600 feet from one end to the other. Its height varies from five stories to 12.

“That is exactly what the modern tenants want: bigger floor plates, higher ceiling heights, lots of light and rooftop decks everywhere,” said John Kilroy, company chairman and CEO. “It’s a 21st century kind of workforce environment.”

Kilroy has bet billions of dollars on San Francisco’s tech expansion since 2010, developing 100 Hooper St., 350 Mission St. and 333 Brannan St., and buying other properties like 100 First St., 360 Third St., and 303 Second St. Kilroy is the developer of the Flower Mart property at Sixth and Brannan, which will total 2.3 million square feet.

The lease comes as big tech leasing has seen a revival in the city, in contrast to a slowdown in leasing among tech startups. While the growth of tech jobs overall has flattened out after six years of rapid expansion, large tech companies continue to make space commitments in San Francisco.

Earlier this month, Facebook announced it had leased a large amount of space at 181 Fremont St., a new mixed-use building of offices, ultra high-end condominiums and a hotel. Other recent deals include expansions by Adobe, Stripe and Twitch. Of 5.4 million square feet of office space under construction in San Francisco, 84 percent has been pre-leased.

Kilroy said Dropbox beat out several other tenants that were ready to locate at the Mission Bay complex.

“I wish I had five more of these — I’d lease two to tech, two to biotech and save one for someone else,” Kilroy said. “This is all happening when Wall Street pundits are saying tech is down and San Francisco’s office market is not going to have any more big absorption. This is turning out to be one of the best years ever.”

Dropbox will take possession of the space in three phases, starting in the fourth quarter of 2018.

“We’re excited to partner with Kilroy to create a new home for our growing team. The Exchange is a space that will reflect our creative culture and inspire us to continue building great products for our users.” said Dropbox CEO Drew Houston, a co-founder of the cloud storage company.

Ted Egan, the city’s chief economist, said 2017 is shaping up to be a stronger year than 2016 for employment growth, although it’s a far cry from 2015, which saw 20 percent growth.

“Year over year it’s pretty flat, but there may be a little bit of an upturn in 2017, associated with the rising stock market and an increase in venture capital,” he said.

And whether or not startups are strong, mature companies like Dropbox, Adobe and Salesforce will continue to grow, he said.

“I don’t think there is any reason to think that the tech boom is over,” said Egan. “It could be getting a third wind.”

J.K. Dineen is a San Francisco Chronicle staff writer. Email: jdineen@sfchronicle.com Twitter: @sfjkdineen