Developers on Brooklyn's Atlantic Yards complex will speed up construction of long-promised housing at below-market rates, city and state officials said Friday.

Construction on hundreds of "affordable" apartments units are set to begin later this year or early next year in the area in the borough's Prospect Heights neighborhood, and more than 2,000 will be built within the next decade, the officials said. Who gets the apartments will depend on income and a lottery of applicants, a statement from Gov. Andrew M. Cuomo's office said.

The developer, Forest City Ratner, has agreed that if construction doesn't begin in the time frame, it would cost the company a penalty of as much as $5 million.

When pitched to the public, the Atlantic Yards project was supposed to feature thousands of housing units that the poor and middle class could afford. But in 2012, only the Barclays Center arena opened -- without a single apartment ready.

The project has been beset by the 2008 economic crash, missed deadlines and litigation.

Mayor Bill de Blasio -- who has promised to create or preserve 200,000 units of affordable housing -- cheered the developments.

"I feel very good about where we stand now," he said.

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