Yosef was born in Warsaw on Shavuot 1926 (5686) to Penina and Tzvi Reshelbach. They made aliyah when he was still a boy, and he studied in the Tachkemoni School.

He joined no political party, but he was an IZL member; after the split, he moved to Lehi. He was arrested by happenstance. He was near the Rama Cinema in Ramat Gan. A Jewish detective who patrolled the area arrested him, started interrogating him, and brought him to the Ramat Gan police station. A Jewish officer was there, and Reshelbach gave a different name and address. They suspected him and one of the people in his company, so they followed him and tracked him to his house. “Get up, get dressed!” the British detectives ordered when they came to arrest him. They suspected him of membership in the underground, though they could not prove it.

Nevertheless, Yosef was imprisoned in Jaffa, in Acre and then in Latrun. He was exiled to Africa with a group of fourteen, in the second such deportation. He arrived on 6 December 1944 and was held in Sembel (near Asmara, Eritrea), Carthago (Sudan), back in Eritrea, and finally Gilgil (Kenya). After the State was established, he was among the last to be returned to Israel, on 12 July 1948. He then joined the IDF and served in the armory of the Infantry Officers Training School, as a private.

Professionally, he worked as a mechanic, independently.

He married Zipporah Gevirtzer, and they had four children: Ehud, Yuval, Hovav and Eyal.

His brother, Avraham Arnon (Reshelbach), was also exiled to Africa.

He never joined a political party or movement after his return.