Uzan was born in Moknine in Tunisia, and was a member of the right-wing Betar movement in his youth. He made aliyah to Israel in 1949 and joined the left-wing Mapai party. He settled in Gilat, serving as the moshav's secretary and treasurer between 1952 and 1959. In 1960 he founded the Negev Moshav Purchasing Company, and managed it until 1968. He also founded the Negev Water and Merhav transport companies.
Between 1970 and 1973 he was secretary of the Moshavim Movement. Despite not being a Knesset member, he returned to the cabinet in 1974 when he was appointed Minister of Communications. After Golda Meir resigned and Yitzhak Rabin formed a new government later in the year, he became Minister of Agriculture. In March 1975 he regained the Communications portfolio in addition to the Agriculture post. Following Likud's victory in the 1977 elections he lost his cabinet position.