Stefánsson commenced his literary career with poetry. He ventured into novel writing in the ’90s, gaining international success. In 2005, his work Summer Light, and Then Comes the Night earned him the Icelandic Literary Award, followed by the Per Olov Enquist Literary Award in 2011. His novel The Fish Have No Feet was nominated for the International Man Booker Prize in 2017, and in 2022, it received the French Prix du livre étranger for the best foreign-language book of the year.