The announcement was made by White and Mayor Michael Bloomberg on Thursday.
The city says it is the largest private donation in city history for the "greening" of New York.
The botanical garden will use the money to create a new native plant garden for the study and display of indigenous species.
The Prospect Park grant will go to restore a 26-acre area to the original design of Frederick Law Olmsted and Calvert Vaux (VAHKS) - who are also the architects of Central Park.
The funds will be made from White's Leon Levy Foundation.
