The experimental solar-powered aircraft, aimed at promoting clean energy technologies, landed at 11:17pm local time (4:17am GMT or 9:47am IST) at Tulsa International Airport after taking off at 3:00am (10:00am GMT or 3:30pm IST) from Phoenix, Arizona, live feed showed.
Piloted by Swiss adventurer Bertrand Piccard, the flight lasted just over 18 hours 15 minutes.
"The flight was very interesting," Piccard said from the cockpit in comments broadcast live just after the landing. "Especially the first part above Arizona and New Mexico, the landscapes were fantastic."
Solar Impulse team member Christoph Schlettig said the flight went "very well."
"This feels like a really great success," he said.
Video showed the plane descending slowly and landing smoothly at night, silhouetted by the flashing lights of airport vehicles.
Objective: New York, ASAP
The plane will make one or two more stops before landing in New York, in the latest leg of a journey that kicked off in Abu Dhabi on March 9, 2015.
"The objective is to reach New York as soon as possible!" the Solar Impulse 2 team said in a statement Wednesday, although it is not clear when the plane might reach there.
Thanks to an inflatable mobile hangar, which can be packed up quickly and transported, Solar Impulse 2 can be sheltered at a variety of locations.
The aircraft was grounded in July last year when its batteries suffered problems halfway through its 21,700-mile (35,000-kilometre) circumnavigation.
The crew took several months to repair the damage from high tropical temperatures during a 4,000-mile (6,437-kilometre) flight between Nagoya, Japan and Hawaii.
The plane was flown on that stage by Piccard's teammate Andre Borschberg, whose 118-hour journey smashed the previous record of 76 hours and 45 minutes set by US adventurer Steve Fossett in 2006.
He took catnaps of only 20 minutes at a time to maintain control of the pioneering plane during the flight from Japan, in what his team described as "difficult" conditions.
The Solar Impulse 2, which weighs roughly the same as a family car but has wings wider than those of a Boeing 747, contains 17,000 solar cells that power the aircraft's propellers and charge batteries.
At night, the plane runs on stored energy.
The typical flight speed is around 30 miles (48 kilometers) an hour, which can increase to double that when exposed to full sunlight.
'Piece of cake'
After crossing the United States, the pilots are set to make a trans-Atlantic flight to Europe, from where they plan to make their way back to their point of departure in Abu Dhabi.
Piccard, a doctor by training, completed the first non-stop round-the-world balloon flight in 1999.
His teammate Borschberg is no stranger to adventure -- 15 years ago he narrowly escaped an avalanche, and in 2013 he survived a helicopter crash with just minor injuries.