The union was formed by the amalgamation of the Amalgamated Metal Workers' Union and the Federated Shipwrights' & Ship Constructors' Association of Australia in 1976, and functioned until 1983 when it joined the Federated Moulders' (Metals) Union of Australia to become the Amalgamated Metals Foundry and Shipwrights' Union.

The Amalgamated Metal Workers Union originally formed in 1973 from the amalgamation of the Amalgamated Engineering Union, the Sheet Metal Working, Agricultural Implement and Stovemaking Industrial Union of Australia, the Boilermakers' and Blacksmiths' Society of Australia, and the Federated Jewellers. In 1976 the union amalgamated with the Federated Shipwrights' & Ship Constructors' Association of Australia to become the Amalgamated Metal Workers & Shipwrights Union. In 1983 it joined the Federated Moulders (Metals) Union of Australia to become the Amalgamated Metals Foundry and Shipwrights' Union. It reverted to the name Amalgamated Metal Workers' Union in 1985 and operated until 1991 when it amalgamated with the Association of Draughting Supervisory & Technical Employees to become the Metals & Engineering Workers' Union.

The union was originally registered as the Amalgamated Tinsmiths' Sheet Metal Workers' Cannister Makers' Gas Meter Makers' & Assistants' Union in 1911 and comprised of unions that had operated since 1881. From 1913 its name changed to the Sheet Metal Working Industrial Union of Australia. In 1945 the union changed its name to the Sheet Metal Working Agricultural Implement & Stove Making Industrial Union of Australia to reflect growing membership from members of the Federated Agricultural Implement & Stovemakers' Porcelain Enamellers' & Ironworkers' Association of Australia. It was deregistered in 1972 and joined the Amalgamated Engineering Union to form the Amalgamated Metal Workers' Union in 1973.

Thomas (Tom) Wright was born in Scotland and emigrated to Australia about 1913 and was apprenticed in the sheet metal working trade at the age of fourteen. Wright joined the Sheet Metal Workers' Union in 1921 and in 1924 was appointed to the New South Wales Branch Executive of the Sheet Metal Workers' Union. He was the NSW Branch Secretary from 1936-1972, and was Federal President of the Union from 1940-1972. Wright pioneered amalgamations of the SMWU with the Jewellers' & Stove Makers' Unions in the 1930s and 1940s and contributed to the formation of the Amalgamated Metal Workers' Union. At the time of his retirement in 1972 he was the NSW State President and National Vice-President of the Amalgamated Metal Workers' Union.

Wright was a promoter of the ACTU in 1926-1927 and was the Sheet Metal Workers' Unions' delegate from 1938 to 1972, serving on the ACTU Executive for many years and on its Shipbuilding Sub-Committee from 1946-1963. He was actively involved on the Executive of the NSW Labor Council from the 1920s until his retirement in 1972. He was a member of the NSW Labor Council delegation which travelled to China and the Soviet Union in 1927. In 1943, Wright helped found the Metal Trades Federation on which he was a Sheet Metal Workers' Union delegate. He visited the Soviet Union again in 1952 and 1969, China in 1952, and in 1963 visited Cuba after the Batista regime was defeated.

Tom Wright and his wife, Mary, played a substantial part in the long campaign to achieve equal pay for women and were active in campaigns on Aboriginal rights.