The Museum of Contemporary Art was established to fulfill the museum aspect of the visionary bequest of Australian expatriate artist John Power (1881-1943), who left his personal fortune to the University of Sydney to inform and educate Australians in the contemporary visual arts. 

The traditional owners of the land on which the MCA building is situated are the Eora people of the Gadigal nation. This site also marks the landing place of the First Fleet in Port Jackson in 1788. In 1802 Sydney's first hospital and wharf were built nearby, with commissariat stores built by Colonel Foveaux in 1812. In the 1930s the commissariat stores and taxation building were demolished to make way for a new Maritime Services Board (MSB) building (the previous MSB offices were displaced by the Cahill Express Way and Circular Quay railway development).

Government architect W.H. Withers began work on the building plans in 1939. Work resumed in 1944 under government architect W D H Baxter after a postponement of four years from 1940 due to Australia’s involvement in World War II. Builders were appointed in 1946 but difficulties in securing labour and material due to post war shortages delayed construction. The foundation stone was laid in 1949 and in 1952 the MSB building opened.

With the relocation of the MSB to larger premises in 1989 the building was gifted by the NSW State Government to the Museum of Contemporary Art. Funded by the University of Sydney and the Power Bequest, restoration and refurbishment of the building commenced in 1990 under the direction of Andrew Andersons of Peddle Thorpe/John Holland Interiors and in November 1991 the Museum of Contemporary Art officially opened.