He was born at the Norwegian naval base Fredriksvern, near the village of Stavern in Vestfold County, Norway. Boyesen grew up in Fredriksvern, then in Kongsberg, and from 1854 at Systrand in Sogn. From 1860 he went to Drammen Latin School, and after his final exams he took another exam at the university in 1868. Boyesen was well-schooled in both German and Scandinavian literature, graduating from the University of Leipzig and the University of Oslo.

Boyesen immigrated to the United States during 1869 and initially became assistant editor of Fremad, a Norwegian language weekly published in Chicago. The multi-lingual Boyesen subsequently taught Greek and Latin classes at Urbana University. Boyesen was a professor of North European Languages at Cornell University from 1874 to 1880. Boyesen became a professor of Germanic languages at Columbia University in 1881. His scholarly works included Goethe and Schiller, Essays on German Literature, A Commentary on the Works of Henrik Ibsen and Essays on Scandinavian Literature.

Through its series of public lectures Boyesen won reputation as an excellent lecturer. He was an immensely prolific writer, in 20 years he published 25 books of novels, short stories, poems and literary criticism, and periodicals were more short stories and a wide range of articles and book reviews. Boyesen is more commonly known for his works of popular fiction. His most successful books have remained those based upon Norwegian culture and habits. He wrote many books of fiction for adults and children and some poetry. He is best remembered for his novel Gunnar: A Tale of Norse Life generally considered to have been the first novel by a Norwegian immigrant in America.