Nęss jr. was born in Germany in 1937 by Norwegian mother Kiki Nęss and father German Raab, a physician and major of the Wehrmacht. Nęss' mother was the sister of philosopher and mountaineer Arne Nęss senior, who had a strong influence on his like-named nephew. Nęss jr's family lived in Germany during World War II, but when his parents were divorced after the war, he moved to Norway with his mother.
In 1966 he married Filippa Kumlin d'Orey of Sweden, and they had three sons together. After the divorce from d'Orey, he had a relationship with Norwegian actress Mari Maurstad. In 1985 Nęss met soul diva Diana Ross on a trip to the Bahamas. He and Ross married in 1985 and got two sons, until parting in 1999. The last five years of his life Nęss lived together with Camilla Astrup of Oslo, Norway, with whom he had two sons.
At the age of 19 Nęss jr. already had twenty first ascents of Norwegian mountains under his belt. He then mostly left this sport and went for a career in the shipping industry. In the seventies he went back to mountain climbing, and in 1985 he led the first Norwegian expedition to Mount Everest, reportedly one of the more successful Everest climbs to have taken place. Also participating was British mountaineer Chris Bonington.
On January 13, 2004, visiting friends while on a business trip, he died in a climbing accident during descent of a peak in the Groot Drakenstein hills near the town Franschoek outside Cape Town, South Africa. According to police reports, Nęss' anchoring equipment loosened from the porous mountainside, leading to a 50 m fall. Arne Nęss Jr. was survived by seven children, his last child born as late as March 2003.
After his death, some media observers noted that Nęss could be said to have died doing what he enjoyed most in life, a quite apprehensible statement judging from the adventurer's obvious love of the mountains. In a television interview in the late 90s, being confronted about the risks of mountaineering, Nęss told the reporter: "If I hadn't liked risks, I would rather have played tennis or golf."