Zohar was born in 1928 to Hava and Dr. Dov Tzel-Zion, in Jerusalem. The parents were traditional and Zionist. For this reason, before he made aliyah, Dov changed the family name from Chelchinsky to Tzel-Zion (Shadow of Zion). This Hebraicization was based on the direction of A.D. Gordon, who was his teacher. In 1924, the parents made aliyah from Poland and settled in Jerusalem. Dov worked as a physician in Hadassah Hospital. He also was the director of the Jerusalem community council.
Zohar had a sister and two brothers. He studied in the Ahad HaAm School and in the Max Pine Professional High School. He supplemented this with other courses.
He was part of the senior Scouts.
He was a Hagana member, but physical difficulties kept him from participating in maneuvers and hikes; he also disagreed with the ideology.
In 1947, he joined Lehi, without telling his family, convinced that its path was correct. In 1948, he was a youth instructor at the Lehi base at Sheikh Munis. When the State was established, he left Lehi. He did not enlist in the IDF, as his health gave him an exemption.
Until 1961 he ran a jewelry factory. Since then, he has run a business protecting materials from corrosion. He married Miriam Rieger. They have three children.