Hägg studied chemistry at Stockholm University from 1922, was a Ramsay Fellow at the University of London in 1926, studying under Frederick G. Donnan. He obtained his PhD in Stockholm in 1929 under Arne Westgren for the work X-ray studies on the binary systems of iron with nitrogen, phosphorus, arsenic, antimony and bismuth. After that he became a lecturer at the Stockholm University and in 1930 at the University of Jena, Germany. In 1937 he became professor of inorganic and general chemistry at Uppsala University. He retired in 1969.
Hägg's research dealt with nitrides, borides, carbides and hydrides of transition metals and determined their crystal structure with X-ray diffraction. He also developed X-ray cameras and calculating machines for this purpose. His investigations into phases and phase transformations in steel had practical applications. In Sweden he is known for his university chemistry textbooks.