Anderson, known commonly by his middle name Noble, was born in Ireland in 1865, and graduated in engineering and arts.
In 1894, Monash and Anderson set up a consulting partnership, which lasted from 1894 to 1902, designing and contracting engineering works.
After a meeting with Frank Gummow of Sydney in 1897, Anderson negotiated an agreement for the firm to become the Victorian agents for reinforced concrete using the Monier patents and won several contracts for bridges using the technology and he and Monash concentrated on building concrete bridges.
In the 1920s he acted as engineering consultant to Walter Burley Griffin, on the design of the Cotter Dam and water supply system for the new capital at Canberra.
He married Ellen Mary White-Spunner and they had six children, including Alice Elizabeth Foley Anderson (1897–1926), businesswoman and owner of the first all-women garage workshop in Australia,.