The building was brought down to open up new views of the Statue of Liberty and create space for a 30-acre park.
The FDNY and Department of Buildings oversaw the controlled implosion, which took about 10 seconds and used 200 pounds of dynamite.
Built in 1968, the building had been used to house Coast Guard families, but had not been in use since 1996.
The implosion is part of a $250 million transformation of Governor's Island that will also include new fields for parks, soccer fields, and baseball fields.
City officials say the implosion at 7:36 a.m. Sunday may have been visible in parts of Manhattan, Brooklyn, Staten Island and New Jersey.
Governors Island, a longtime military base, is in New York Harbor off the tip of lower Manhattan. The city now controls the island and is redeveloping it, with some of it becoming parkland.