The Pritzker Prize-winner's plans integrate three existing landmark buildings with three pavilions.
According to the architect, the modest scale of the building - which doubles as a museum - is respectful to its traditional architecture and the surrounding neighbourhood.
It achieves this by locating more than 50 per cent of its space below ground.
The project is Piano's first New York City commission to be completed and adds about 8,000m 2to the library's space.
Key features of Piano's work include a dramatic new entrance on Madison Avenue; a spacious central 'piazza'; new and renovated galleries; a new 280-seat performance hall; a naturally lit reading room; and storage space to store the library's collections.