During his childhood, he moved to Skien, in the south of the country, where he studied at the Latin school. In 1873, he graduated and obtained an Examen artium with Latin honor laudabilis præ cæteris. Then, he studied at the Great Technical School in Germany, but he resigned and chose to study classical philology.
He graduated in 1881.
He is mainly known for his translations of Homer"s epic poems, the Illiad and the Odyssey. He was also known as classical languages teacher and as militant for learning of Latin language at school. He was an education official in Fredrikstad between 1894 and 1910 and in Drammen between 1910 and 1926.
The same year, he obtained a scholarship for his classical philology studies, and wrote an elementary thesis in German, entitled Die Zahl der Bürger von Athen im 5.
Jahrhundert ("The number of inhabitants in Athens in the 5th century"). Instead of having career in science, Østbye chose to work as a teacher.
In 1894, he was hired as director, and then became chancellor of Fredrikstad høiere almenskole in 1898. In 1910, he became chancellor at the Latin school of Drammen until he retired in 1926.
Peter Østbye was described as a calm and agreeable person and as a good chancellor.
Even though Østbye published a translation of Sophocles" Oedipus at Colonus in 1891, he performed most of his translation work within the last decades of his life. When he released a translation of Illiad in 1920, he was already 65 years old. He also redacted articles about the evolution of Norwegian schools for German press
In 1927, a Festschrift named Tidskrifte ("newspapers" or "gazettes") was published in tribute to Østbye and four of his co-workers.
The Rektor Østbye street of Fredrikstad and the Peter Østbye street of Drammen are both named in tribute to Peter Østbye.
He was also member of Undervisningsrådet ("Teaching Council") during 15 years.