Rhéaume ran unsuccessfully for a seat in the House in March 1962, but he was elected to represent the opposition Progressive Conservatives in the Northwest Territories one year later when Lester Pearson was the Liberal prime minister.
He served on nine Parliamentary committees, including fisheries, Indian affairs, human rights and citizenship, as well as mines, forests and waters.
He was defeated in the 1965 and 1974 federal elections, and according to the parliamentary website, worked as an administrator, insurance agent and social worker.
The congress' National Chief Betty Ann Lavallée says Rhéaume was an honorary member of the organization and a member of the Aboriginal Order of Canada.
She has offered her condolences to the family, saying his contributions will live on, and he will not be forgotten.
The cause of death was unknown.
Note to readers: This is a corrected story. A previous version wrongly said Rheaume was the first elected MP since Louis Riel.
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