The plane left Washington for New York's John F. Kennedy airport just before 5 a.m. Saturday, the BBC reported.
Pilot Andre Borschberg said he anticipated the journey would take about 21 hours.
The transcontinental flight began in May in San Francisco, and has made stops in Phoenix, Dallas and St. Louis.
JFK is to close two of its runways to accommodate the plane's arrival, The Wall Street Journal reported.
"It's difficult to plan this because of all the traffic at JFK and since this is a completely experimental plane," said Borschberg, a businessman and engineer who trained as a pilot in the Swiss air force.
The plane, which cost about $8.5 million to make, has a wingspan of 208 feet -- the same as an Airbus A340, which seats more than 400 passengers -- but weighs just 3,500 pounds, roughly the same as a mid-size sedan, and has a top speed of 45 mph.