He was a Quebec Conservative Party leader, but never Premier (he lost the 1912 election, and Lomer Gouin became Premier of Quebec). He was in the Legislative Assembly of Quebec from 1892 to 1916, as a Member for the riding of Joliette. After his studies at Université Laval, he was admitted to the Barreau du Quebec and he practiced law for over 15 years.
He was mayor of Joliette from 1903 to 1910, and, in 1916, he became a Quebec Superior Court judge.
He was Chief Justice of Quebec from 1932 to 1942. He was Knighted by King George V in 1934.
Sir Joseph-Mathias Tellier is the brother of Louis Tellier, the father of Maurice Tellier, the grandfather of Paul Tellier, and a first cousin of Raymond Tellier, who is the grandfather of Luc-Normand Tellier. He lost the 1912 election against Sir Lomer Gouin.