"It's a project for energy, for a better world," Swiss pilot Bertrand Piccard told journalists standing in front of the plane which weighs no more than a large car but has the wingspan of a Boeing 747.
The plane was scheduled to depart at 1 am Cairo time for Abu Dhabi.
It had been due to leave Cairo last week but was grounded because of strong winds and Piccard falling ill.
The pair have alternated legs of the journey, with Borschberg piloting the flight's Pacific stage, a 6,437-kilometer flight between Nagoya, Japan and Hawaii.
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The 118-hour leg smashed the previous record for the longest uninterrupted journey in aviation history.
The plane set out on March 9, 2015 from Abu Dhabi, and has been across Asia and the Pacific to the United States and on to Spain and Egypt with the sun as its only source of power.
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."
It typically travels at a mere 48 kilometers per hour, although its flight speed can double when exposed to full sunlight.
The plane arrived in Cairo after a two-day flight from Spain, finishing the 3,745 kilometer journey with an average speed of 76.7 kilometers an hour.
It had earlier landed in Seville after completing the first solo transatlantic flight powered only by sunlight.
Piccard said the last leg of the tour would be difficult.
"It's a very very hot region... Its going to be an exhausting flight," he said.
Piccard, a psychiatrist, made the first non-stop balloon flight around the world in 1999.
Borschberg, meanwhile, only narrowly escaped an avalanche 15 years ago and in 2013 survived a helicopter crash with minor injuries.