Six parking lots in downtown Los Angeles recently sold for $82 million. But the buyers aren't interested in the parking business: They want to build 1,500 rental apartments on the properties.

The deal is the latest evidence that Los Angeles's downtown revival, which began a little more than a decade ago, is picking up momentum as a number of residential developers rush to build rental housing. Some real-estate executive were initially skeptical that people would trade in their cars and suburban bungalows to live downtown, but demand for such housing has turned out to be stronger than many expected.

Mack Real Estate and AECOM Capital want to replace downtown L.A. parking lots with apartments.Cushman & Wakefield

"Not everyone has to live in New York to live without a car," said Richard Mack, chief executive of Manhattan-based Mack Real Estate Group, which teamed up with AECOM Capital to acquire the parking lots. "People want to live near their jobs and their friends."

A dearth of apartments is fueling one of the city's largest building booms in years. There are about 14,000 apartment units in downtown Los Angeles. About 5,100 units are under construction, and more than 3,400 units were built between 2008 and 2013, according to Polaris Pacific, a real-estate sales, marketing and research firm. More than 3,000 additional rental units have been approved, with another 7,000 proposed. Meanwhile, there are only 17 condo units for sale and 68 under construction.

"A lot of smart people are saying, 'Now is the time for downtown L.A., for multifamily rental,' " said Mr. Mack, who is part of a New York real-estate family.

In Los Angeles, many locals credit the Staples Center, a sports arena and entertainment venue that is home to the Los Angeles Lakers and other teams, with jump-starting the change in 1999. In 2007, the first phase opened of L.A. Live, an entertainment district with a Ritz-Carlton hotel and numerous eating options, including a Wolfgang Puck Bar & Grill. In recent years, some 300 bars, clubs and restaurants have opened in the area, said Carol Schatz, president of the Downtown Center Business Improvement District. Whole Foods Market Inc. WFM +0.23% expects to open its first downtown Los Angeles store in 2015, which many said is a game-changer for an area that offers minimal food shopping options. "This is a revolution," Ms. Schatz said. "We had a functioning downtown up until the '40s and then the car culture grabbed us by the throat and almost choked us to death." Sentiments have changed, she said, because "we have given people a reason to live downtown."

With more people flocking downtown, the vacancy rate for apartments has fallen. In the third quarter, downtown Los Angeles had a vacancy rate of 3%, down from 3.3% in the prior quarter, according to Marcus & Millichap Real Estate Investment Services. In the past year, the vacancy rate has fluctuated between the mid-2% and mid-3% range. Average rents, meanwhile, were $1,970 a month in the third quarter, up 3.8% from the prior-year period. The national apartment vacancy rate is 4.2%, while average rents are $1,073, according to research firm Reis Inc.

Equity Residential, EQR +0.23% one of the nation's largest publicly held owners of apartments by number of units, plans to open early next year the Jia Apartments, which will have 280 units. Private-equity firm Carlyle Group CG -1.69% LP also expects to open the 430-unit Avant, its first downtown Los Angeles community, early next year. Associated Estates Realty Corp. AEC -1.70% , a public company that has long focused on middle America, is at work on two L.A. developments that will have about 645 units.

To be sure, the robust development pipeline has some worried that oversupply could push up vacancy rates and depress rents. Moreover, some industry watchers point out that rental growth is slowing in many cities nationwide, just as land prices and development costs rise, making new construction a less likely bet. And given apartment buildings typically take a year or more to build, developers risk delivering supply into an uncertain market.

"I might face a little bit more competition when I open," Mr. Mack said, adding he plans to own for the long term.

Other developers share his confidence. "We're not late in the cycle in downtown L.A. because they don't have enough apartments to begin with," said Jeffrey Friedman, chief executive of Richmond Heights, Ohio-based Associated Estates Realty.

Mack Real Estate Group, through West Coast affiliate Mack Urban, and AECOM Capital, an investment fund of Los Angeles-based AECOM Technology Corp., both put up 50% equity for the deal. Tishman, an AECOM division, will manage construction when it begins next year. Paul Keller, a Mack Urban founding principal, said the project will include outdoor spaces and amenities, including a gym, pool deck and spa. Rents for studios and one-bedroom units are expected to be in the mid-$2,000 range.

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