Born in Germany in 1947, Katz immigrated to Israel in 1949. After finishing school and national service he worked as an electronics technician. He became involved with trade unions when he became a member of the workers' council at Israel Aerospace Industries in 1983, and was also chairman of the technicians and engineers' union. In 1993 he became secretary of the National Workers Union of Israel Aircraft Industries, and was appointed chairman of the pension funds policy team of the Histadrut in 1996. Katz founded the Oz (Hebrew: עוז, lit. Strength) faction within the Histadrut.
In 1999 Katz joined the new One Nation party. He was placed second on its list for the elections that year, and was elected to the Knesset when the party won two seats.
Shortly before the 2003 election, he defected to Likud and was placed 37th on its list. He was re-elected as the party won 38 seats. As a Likud MK he was appointed Chairman of the Labour, Welfare and Health Committee. He also initiated a bill banning MKs from serving as head of the Histadrut, meaning Peretz had to resign from his post in the union.
In the Likud primaries for the 2006 election, Katz gained thirteenth place on the party's list. Likud won only twelve seats and he lost his seat. However, when Natan Sharansky resigned from the Knesset in November 2006, Katz replaced him as the next member on the list. He retained his seat in the 2009 elections, for which he was placed fourteenth on the Likud list. He was re-elected again in 2013 and 2015, after which he was appointed Minister of Welfare and Social Services in the new government.