Vilhjalmsson was born in Edinburgh, Scotland in 1925. He studied at the University of Iceland in 1944-1946, at the University of Nottingham in 1946-1947 and at the Sorbonne in Paris from 1947-1952. He worked as a librarian at the National Library of Iceland in 1953 and at the National Theatre 1955-1957. He was involved in many art groups and events including the Reykjavik Writers Festival, the Writer's Union of Iceland, the Federation of Icelandic Artists, the Reykjavík Arts Festival, the Reykjavík Film Festival and the Reykjavík Judo-Society.