"The Board must resign now, and make way for a more representative Board to take over the public broadcaster, and run it in the interests of the majority of South Africans," said spokesman Patrick Craven.
This call comes a day after the Johannesburg High Court denied the board leave to appeal a finding that its suspension of group chief executive officer Dali Mpofu was unlawful.
Craven said the union welcomed the court's decision and also noted a memorandum signed by seven members of the broadcaster's executive staff expressing no confidence in the board over its handling of Mpofu's case.
"Add to this the vote of no confidence by the Parliamentary Communications Committee and the ongoing campaign by Cosatu and many other civil society organisations for a more representative SABC Board, and you see an overwhelming public demand for change," said Craven.
Cosatu also welcomed the proposal by Communications Minister Ivy Matsepe-Casaburri for a review of legislation governing the SABC.
Speaking in the National Assembly during debate on her budget vote on Tuesday, Matsepe-Casaburri also suggested that the parliamentary committee consider leading a public hearings process on the public broadcaster best suited to an emerging democracy.
The findings would also inform the legislative processes in the department, she said.
"The federation will be glad to participate in public hearings and submit proposals for ways to ensure that the Board is appointed in a more open and transparent manner and that its members are drawn from all sections of the population, including the labour movement," said Craven.