The plane, which took off from New York's JFK airport around 2:30 am (0630 GMT), is piloted by Swiss adventurer Bertrand Piccard, who is expected to spend approximately 90 hours -- during which he will take only short naps -- crossing the Atlantic.
"It's my first time taking off from JFK," Piccard said over a live feed from the aircraft as he headed off into the night sky en route to Spain's Seville Airport.
As of 9:30 pm in New York (0130 GMT Tuesday), the plane was near Canada's Nova Scotia and turning east to begin its ocean crossing after hugging the North American coast during the day.
Piccard noted in a blog post that he gets to experience a "Strawberry Moon" from the plane -- an astrological phenomenon that occurs when there's a full moon on the Summer Solstice, the longest day of the year.
He will have "a bright full moon to guide me across the Atlantic Ocean in my solar-powered airplane."
The voyage marks the first solo transatlantic crossing in a solar-powered airplane and is expected to last four consecutive days and nights, depending on weather.
The plane, which is no heavier than a car but has the wingspan of a Boeing 747, is being flown on its 22,000-mile (35,400-kilometer) trip in stages with two pilots -- Piccard and Swiss entrepreneur Andre Borschberg -- taking turns at the controls.
The pair have flown alternating legs of the journey, with Borschberg piloting the flight's final Pacific stage, a 4,000-mile flight between Japan and Hawaii.
The 118-hour leg smashed the previous record for the longest uninterrupted journey in aviation history.
The plane, now on the 15th leg of its east-west trip, set out on March 9, 2015 in Abu Dhabi, and has flown across Asia and the Pacific to the United States with the sun as its only source of power.
"Smooth takeoff and all #Si2 systems have been checked here at the Mission Control Center for the #Atlantic Crossing," Borschberg posted on Twitter soon after Solar Impulse 2 was off the ground.
A few hours into the flight, which could be tracked via internet on the solarimpulse.com website, the flight team wrote that the flight was blessed with "a beautiful day without a single cloud."
In another post about seven hours into the flight, Piccard described spotting a cluster of whales in the ocean waters.
"What a beautiful sight of jumping whales. Just like the whales below me, #Si2 depends only on nature," he wrote, as a live video feed on the website captured his every movement at the controls of the aircraft.
Prince Albert of Monaco, a patron of the project, gave the flight the go-ahead from its mission control center in Monaco, telling Piccard "you are released to proceed."
Approximately a third of the journey still remains for the plane, which will fly through Europe and on to Abu Dhabi after crossing the Atlantic.
The single-seat aircraft is clad in 17,000 solar cells. During nighttime flights, it runs on battery-stored power.
"Solar Impulse is like a flying smart grid, and if we can make it work in an airplane, where we can't cheat, we can make it work on the ground, in our cities, for our homes and for all applications," Borschberg said in a
The plane typically travels at a mere 30 miles per hour, although its flight speed can double when exposed to full sunlight.
"Best of luck on this wonderful adventure @bertrandpiccard & all the team," British billionaire entrepreneur Richard Branson, owner of space tourism company Virgin Galactic, posted on Twitter.
Piccard and Borschberg are no strangers to adventure.
Piccard, a psychiatrist, made the first non-stop balloon flight around the world in 1999. Borschberg narrowly escaped an avalanche 15 years ago and in 2013 survived a helicopter crash with minor injuries.