He was the son of the artist Clara Olsson and in his early youth, he had been a student of painter Helmer Osslund but was largely self-taught as an artist. He studied law and for a short time, he served as attaché at the Ministry of Foreign Affairs. In 1921, he joined the National Museum as a teaching assistant, whose collection of modern paintings and sculptures he later headed from 1932 to 1937. From 1923 to 1924 he was secretary of the committee for supporting artistic activities in Sweden, was a commissioner for several exhibitions, including in Paris in 1927 and 1929, and compiled a catalogue of the National Museum's painting collection in 1936.
He painted mainly city views of Stockholm and Uppsala, as well as landscapes whilst travelling in France, Italy, Spain and Holland and was known for his portraits of national Swedish worthies including most of their Royal family. Gunne belonged to a group of artists that was known as “Optimisterna” (“Optimists”). For many years, he travelled to France annually, and was influenced by Neorealism and Classicism there. He represented Sweden as a fine artist at the infamous 1936 Berlin Olympics and became a full time painter the following year.
His work is represented in the Swedish National museum and the Prins Eugens Waldemarsudde in Stockholm as well as Museums in Helsinki, Antwerp, Budapest and the World Bank in Washington.