Snorri was born in Hvanneyri, Borgarfjörður. He lived in Norway for a long time and studied art at the Art Academy of Oslo under the direction of Axel Revold from 1931 to 1932. His first publication was a novel written in Norwegian in 1934, but he is known for his poetry books in Icelandic. He was awarded the Nordic Council Literature Prize in 1981 for his poetry collection Hauströkkrið yfir mér. Snorri was a librarian at the Reykjavik City Library (Borgarbókasafn Reykjavíkur) after he moved back to Iceland. From 1942-1966 he served as City Librarian, taking over the post from Sigurgeir Friðriksson.