The Research Expedition Vessel , built in conjunction with the World Wildlife Fund, will be able to hoover up around 5 tons of plastic a day which will then be recycled.
According to one media report the ship will be the world's largest of its type, able to carry 60 scientists and 40 crew.
"The REV will be a platform for gathering knowledge," Røkke told Business Insider.
"I would like to welcome researchers, environmental groups, and other institutions on board, to acquire new skills to evolve innovative solutions to address challenges and opportunities connected to the seas."
A recent study revealed that an uninhabited island in the South Pacific was covered in an estimated 38 million pieces of plastic.
Fisherman to billionaire
Røkke, who suffers from dyslexia, has no secondary or higher education and according to reports worked several years on Alaskan trawlers from the age of 18.
In the 1980's he ran several U.S. companies in the Seattle area before returning to Norway to build a shipping fleet.
Røkke now owns nearly 67% of publicly traded Aker, a shipping and offshore drilling conglomerate, and in the latest Forbes rich list is estimated to be worth $2.6 billion.
After a 2005 conviction for the illegal purchase of a boat licence, Røkke served around 25 days of a 120-day sentence in a Norwegian prison.