SBS was established as an independent statutory authority on 1 January 1978 under the Broadcasting Act 1942. In 1991 the Special Broadcasting Service Act (SBS Act) came into effect and SBS became a corporation.

The Ministers responsible are Senator the Hon. Mitch Fifield, Minister for Communications and the Arts (to 29 May 2019) and the Hon. Paul Fletcher MP, Minister for Communications, Cyber Safety and the Arts (from 29 May 2019).