The project will turn the waterfront complex into a mixed-use development with residential, commercial, incubator, tech and creative space.
A council spokeswoman said the vote passed 47-0, with one abstention. The final vote came after the development firm Two Trees Management agreed to increase the amount of affordable housing available at the site.
According to the revised proposal, 700 units out of more than 2,200 apartments will be designated for affordable housing.
In April, the City Council's Land Use Committee reached an additional deal. It was established that the development's affordable housing would only be leased to tenants making 70 percent or less of the area's median income.
"Eighteen months ago we took a big gamble, passing up an approved plan and going back through the political process because we wanted to build something innovative and worthy of the magnificent site and the dynamic neighborhood," Two Trees spokesman David Lombino said in a statement.
City Council member Stephen Levin said in a statement that the agreement would build on gains made by Mayor Bill de Blasio's administration to maximize affordable housing and open space for Williamsburg.
"By working collaboratively with the Administration, we were able to secure housing that has deeper affordability and will be more accessible to families," Levin said.
Construction on the first building at the site is slated to start in December, city planning officials previously said. Two Trees could not confirm the exact start date of the project at this time.