After graduating from high school he studied music. In 1931 he left Germany, living in Paris, London, Tunis, Algiers and Cuba, before settling in New York. He earned a living playing the piano in a bar, and wrote and composed for revues and cabarets. He then worked for Irving Berlin as a stage manager and production assistant, and for Orson Welles Mercury Theatre company as an assistant director.
Van Eyck went to Hollywood where he worked as a truck driver. He initially found radio work with the help of Billy Wilder, who later gave him small film roles. In 1943 he took US citizenship and was drafted into the army. At the end of the war he returned to Germany as a control officer for film and remained there until 1948 as director of the film section. In 1949 he appeared in his first German film Hallo, Fräulein!
He gained international recognition with a lead role in the 1953 film The Wages of Fear. He went to appear in episodes of several US TV series including The Adventures of Ellery Queen and Alfred Hitchcock Presents. In English-language films he was most often typecast as a Nazi or other unsympathetic German type, while in Germany he was a popular leading man in a wider range of films, including several appearances in the Dr. Mabuse thriller series of the 1960s.
Van Eyck was married to the American actress Ruth Ford in the 1940s. With his second wife, Inge von Voris, he had two daughters, Kristina, also an actor, and Claudia.