Clad in bronze, blackened stainless steel and marble, the skinny residential tower will rise 1,000 feet (304 metres) at 340 Flatbush Avenue in downtown Brooklyn.
Plans were initially unveiled in November 2015, but the project has been awaiting approval from the Landmarks Preservation Commission before work could start.
The design incorporates the landmark-designated Beaux-Arts Dime Savings Bank building into its base, and requires the partial demolition of the rear of the historic structure.
But the architects said that the approval process went smoothly. "We didn't get any opposition," SHoP co-founder Gregg Pasquarelli told Dezeen.
"The community board voted unanimously in favour of it, and Landmarks [Landmarks Preservation Commission] voted unanimously in favour of the building."
The old bank is set to become a retail arcade, while the tower above will be filled with rental apartments, 20 per cent of which would be set aside for below-market rents.
This bucks the trend for luxury condominiums in New York, which are springing up all over the city.
SHoP's own supertall tower in Manhattan is also currently under construction. Named 111 West 57th Street, the tower will rise 1,428 feet (435 metres). Work began last year and is slated to complete in 2018.
The firm's other projects in the city include a pair of bent skyscrapers connected by a skybridge, which is underway beside the East River, and a proposal for New York's tallest timber-framed building.