The plane, which is no heavier than a car but has the wingspan of a Boeing 747, is being flown on its 35,000 kilometer round-the-world journey by two pilots taking turns, Swiss entrepreneur Andre Borschberg and psychiatrist Bertrand Piccard.
"It's absolutely incredible," said Borschberg over a live video feed as the iconic statue lit up the night below him. "It's a dream here."
The light, slow-moving aircraft landed at New York's John F Kennedy International Airport, one minute ahead of schedule at 3:59 am after a five-hour flight from Lehigh Valley in Pennsylvania.
"I felt like a three-year-old kid looking at the Christmas tree, it was so beautiful," Borschberg told a news conference after landing.
It was the 14th leg of an east-west journey that began March 9, 2015 in Abu Dhabi, and has taken the aircraft across Asia and the Pacific to the United States with the Sun as the plane's only source of power.
The journey so far included a stretch of five nights and five days from Japan to Hawaii, which broke a record for the longest uninterrupted journey in aviation history.
The single-seat aircraft is clad in 17,000 solar cells. During night-time flights it runs on battery-stored power.
It typically travels at a mere 48 kilometers per hour, although its flight speed can double when exposed to full sunlight.
Piccard, a balloonist who made the first non-stop balloon flight around the world in 1999, talked about the symbolism of the Statue and changing definitions of liberty during the course of history.