Castle was born in Dresden and attended from 1928 to 1931, the Rabbinical Seminary of the Jewish Synagogue Adass Yisroel in Berlin and the University of Berlin. In 1933 he received a doctorate in philosophy at the University of Leipzig. He continued his studies at the Rabbinical Seminary in Berlin and in 1938 was a rabbi. In 1939 he emigrated to Palestine and was a research fellow at the Hebrew University of Jerusalem.
Josef Burg married in 1949 Riva Slonim and together they have three children: two daughters and a son Avraham Burg. During his last visit to the Knesset he was present as a spokesman for the 15th Knesset in Einschwörung his son.
In Israel, Burg joined the HaPo'el haMisrachi, a moderate- left religious Zionist party. In addition to three other religious parties, Hapoel HaMisrachi could be chosen in the first Knesset elections in 1949 on a common list (United Religious Front). The list won 16 seats and the castle was a seat in the Knesset and became its Deputy Speaker. In the Cabinet formed by David Ben- Gurion was castle Minister of Agriculture and Minister of rationing and supply. After breaking the coalition castle was not taken into account in the new coalition government.
In the elections 1951 the party HaPo'el haMisrachi approached alone and won eight seats. Castle remained in the Knesset and became Minister of Health of the third government. During the further term of the second Knesset castle served as Postmaster General in the fourth, fifth and sixth government.
After the third parliamentary elections on July 26, 1955 Castle was re-elected to the Knesset and. During the coalition negotiations again Postmaster General in the seventh and eighth Cabinet The Office of the Postmaster he retained until 1 July 1958.
In June 1956, the Hapoel HaMisrachi merged with its ideological twin, the Mizrachi Party to the National Religious Party ( NRP). Its chairman, he was in 1970, as the successor of Chaim Moshe Shapira, and held that office until 1986. This year he resigned from all his offices.
Josef Burg was elected to the 1984 elections (11th Knesset) again. He took over the post of welfare minister in the 9th, 10th, 11th, 12th, 13th, 14th and 15th government. In the 15th government, he took over on 1 September 1970, the Ministry of the Interior by the late Chaim - Moshe Shapira and gave it the Welfare Ministry to Yaakov - Micha'el Chasani from. The Interior Ministry, he headed during the 16th, 17th, 18th, 19th and 20th government. During the 17th government, he took over on July 29, 1975 to November 4, 1975 additionally, the Ministry of Welfare. In the 19th, 20th and 21st government, he was also Minister of Religion.
In 1977 he was the president of the World Mizrachi movement.