The Solar Impulse took off from Madrid at 0322 GMT ( 11:22 p.m.) on Tuesday and landed at Rabat's International airport after a 19-hour flight.
Shortly before Swiss pilot Bertrand Piccard landed in Rabat's airport, the project co-founder and pilot Andre Borschberg said the aircraft has proved its sustainability.
"The aircraft can now fly day and night. It's quite a show ... It's a technology we can trust," he told reporters.
Pilot Piccard descended from the plane, smiling as he was greeted by Borshberg and Mustafa Bakkoury, the head of Morocco's solar energy agency.
The Solar Impulse project began in 2003 with a 10-year budget of 90 million euros ($112.18 million) and has involved engineers from Swiss lift maker Schindler and research aid from Belgian chemicals group Solvay.
On Tuesday, the aircraft crossed the Gibraltar Strait separating Africa and Europe at one of its narrowest points. The flight is crucial for the project's developers because it would help improve the organization of a world tour planned in 2013.
The plane, which requires 12,000 solar cells, embarked on its first flight in April 2010 and completed a 26-hour flight, a record flying time for a solar powered aircraft, three months later.
It made its first international flight last month when it completed a 13-hour flight from the western Swiss town of Payern to Brussels.
With an average flying speed of 70 km/h (44 mph), Solar Impulse is not an immediate threat to commercial jets, which can easily cruise at more than 10 times the speed. A flight from Madrid to Rabat can take a little more than an hour.
Project leaders acknowledged it had been a major challenge to fit a slow-flying plane into the commercial air traffic system.
(Reporting By Souhail Karam; Editing by Vicki Allen)