He started his schooling in Hamburg before his family migrated to Australia and he continued his education in Bundaberg and at Maryborough Grammar School before commencing practice as a solicitor. He was a partner in Hamilton and Nielson, Solicitors, and a director of several companies including the Bundaberg Foundry Company, the Blair Athol Coal and Timber Company, the Bundaberg Newspaper Company, and the Yeppoon Plantation Estate Company Limited.
Representing the Labour Party, Nielson contested the seat of Musgrave at the 1902 state election, losing to the Ministerialist candidate, William O"Connell.
After O"Connell died in 1903, Nielson contested the subsequent by-election, this time losing to the Opposition candidate, John White.
Nielson"s third attempt at winning Musgrave came at the 1904 state election, this time defeating White. He held the seat for three years before White regained it at the 1907 state election.
In September of that year, he was appointed by the Kidston Ministry to the Legislative Council and remained a member till the Council was abolished in March 1922.