Røkke started out as a Fisherman aged 18, and has no secondary or higher education. In 1979, he moved to the U.S. to work on fishing trawlers in Alaska. Working as a Fisherman, he saved up enough money to buy his first trawlers. He eventually owned the American Seafoods Company. Røkke was based in Seattle, Washington in the 1980s, owning and operating American Seafoods Company and Resource Group International (RGI), which included Brooks Sports and Helly Hansen. In the mid-1990s, Røkke returned to Norway. In 1996, Røkke become Aker’s main shareholder and a driving force in the company’s development when RGI purchased enough Aker shares to become Aker’s largest shareholder; the two companies subsequently merged. The merger between RGI and Aker was completed in January 1997. Through Aker, Røkke gained an important position within fisheries, and acquired the long-established fishery Business J.M. Johansen with roots back to 1876. Real estate and shipyards is also part of the new company portfolio.
Røkke, along with his Business partner Bjørn Rune Gjelsten, also bought into Wimbledon Football Club in the late 1990s, becoming a joint owner of the team in 2000. The following year, with the side homeless since leaving their Plough Lane ground in 1991 and playing at Crystal Palace's Selhurst Park stadium in Croydon, southeast London, Røkke and Gjelsten, along with chairman Charles Koppel and businessman Pete Winkelman agreed to relocate the team from London to Milton Keynes, a town around 60 miles from their traditional base. The move was controversial and sparked a year of protest at matches from Wimbledon fans, determined not to let their club be 'franchised' like this. Although Common in American sport, the relocation of a professional English football club had never been done before. After rejections from the Football League and The FA, the decision was eventually passed on to a three-man arbitration panel, the outcome being two to one in favour of the move. Wimbledon fans, outraged with the decision, agreed to form a new club to support, AFC Wimbledon, and declared a boycott on their former team. The following season, Wimbledon FC would go on to play in front of record low crowds, including just 664 for a League Cup game against Rotherham, before finally completing the move in September 2003. It renamed itself a year later, adopting the name Milton Keynes Dons.
Røkke is also known for his involvement in association football, and became involved with Norwegian side Molde FK in 1993. He was also central to the funding of the club's new stadium, which got the nickname "Røkkeløkka" (English: "The Røkke Park"). Some estimates suggest that he has spent about NOK 400 million funding the club.
After his 2005 conviction for corruption involving the illegal purchase of a boat licence, Røkke served 24–25 days of a 120-day sentence in Hof Prison, and was subsequently released on parole.
In 2006, Røkke won the “Peer Gynt of the Year” award. He was elected to receive the award by the parliamentary representatives. Persons and institutions that have made a positive impression of the socially beneficial plan and made Norway known abroad can get the Peer Gynt statue.
He has been based in London, England since at least 2007.
Røkke is known for having several exclusive cars, including a Ford GT acquired in August 2016.
In May 2017, Røkke and his wife joined the Gates-Buffett The Giving Pledge, an elite network of big philanthropic givers. Pledge members promise to devote the majority of their wealth to philanthropic causes during their lifetimes or after their death.
Together with his wife, Anne Grete Eidsvig, Røkke has established the Aker Scholarship in partnership with Aker ASA to support Norwegian students' graduate studies at internationally leading universities. Aker Scholarship’s objective is to inspire recipients to make a difference in the development of Norwegian Business, industry, and society for the benefit of generations to come. Røkke's family’s company, TRG, finances Aker Scholarships through donations to their Foundation of Education; Aker administers the scholarship program. The purpose of the Aker Scholarship is to offer highly qualified candidates, with a strong link to Norway, an opportunity to pursue an advanced degree at one of the world´s leading universities, and to support the development of the scholar’s social commitment.