The aircraft was grounded in July when its batteries were damaged halfway through its 21,700-mile (35,000-kilometer) circumnavigation of the globe.
The crew took several months to repair the damage caused by high tropical temperatures during a 4,000-mile flight between Nagoya, Japan and Hawaii.
The plane was flown on that stage by 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 just 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.
– How it works –
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 an hour, which can increase to double that when exposed to full sunlight.
After crossing the United States, the pilots are set to make a transatlantic 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.