The state yesterday voted to officially turn control of the long-delayed Brooklyn Bridge Park project over to the city — helping stabilize the 85-acre plan with much-needed cash and ensuring the park can stay open longer each day.

The Public Authorities Control Board’s vote ratified a plan the Bloomberg and Paterson administrations agreed to in March, in which the state hands over control in exchange for the city filling $55 million of the project’s roughly $120 million budget shortfall with money set aside for the stalled Javits Center expansion.

The park is being built piecemeal as funds become available, with the first sections at Piers 1 and 6 in Brooklyn Heights open since April.