He made his first movie appearance as a child in the 1937 Norwegian classic Fant. His stage debut came reciting poetry at the Norwegian theatre Chat Noir in 1945. He joined the Norwegian National Theatre in 1946 and become one of its most prominent figures, appearing in 64 different roles the next 60 years.
As late as 2006 he co-starred with Toralv Maurstad in an adaption of Waiting for Godot.
Skjønberg"s first starring role in films was in 1951"s Vi village skilles. Throughout the years he has acted alongside Tom Courtenay, Nigel Hawthorne, Susannah York, Edward Woodward, Gérard Depardieu, and co-starred with Hollywood veterans Cliff Robertson and Robert Mitchum in the 1995 movie Pakten.
He also found popularity with new generations heading the cast of Familiesagaen De Syv Søstre (1996–2000), one of Norway"s first major soap operas. In the show Skjønberg co-starred with his real-life wife, actress Mona Hofland.
He was also popular as the old mountain gnome Erke in the widely successful children"s series July i Blåfjell (1999).
He is the son of actress Henny Skjønberg.