Oluf Rygh was born in Verdal. His parents were Peder Strand Rygh (1800-1868) and Ingeborg Marie Bentsen (1809-1878). He was the older brother of Evald Rygh and Karl Ditlev Rygh. Oluf Rygh attended the Trondhjem Cathedral School in 1850 and went to the University of Christiania to study philology, where he graduated in 1856. In 1858, while a teacher at Nissens Skole in Christiania, he was a research fellow for history. Later he was a professor of classical philology, history and Scandinavian languages.
Rygh was professor of history at the Royal Frederick University between 1866 and 1875. He was director of Oldsaksamlingen (which subsequently became the Museum of Cultural History) from 1862 and professor of Nordic archaeology from 1875 - the first professor of archaeology at any Scandinavian university. He led excavation of the Tune ship 1867. His work Norske Oldsaker (Norwegian Antiquities) published in 1885 is recognized for its detailed illustrations and even today is still a significant reference source.
Oluf Rygh is best known for creation of Norske Gaardnavne (Norwegian Farm Names), which is a 19 volume set of books based on a manuscript prepared from 1897 to 1924. The book contains a standardized notation, information on pronunciation, historical forms and the etymology for recorded farm, estate and manor names in Norway, which became the standard for place names in Norway. It inspired similar research in Sweden and Denmark. Rygh died in 1899 at Ulefoss in Holla, Telemark. At the time of his death, only three and one half volumes had been published.
His more significant publications include: