Ritchie was a scion of prominent families—the Almons, Ritchies, and Stewarts were all major families in Nova Scotia—and his brother, Charles Ritchie was an important Canadian diplomat and diarist. Ritchie's great-uncle, Sir William Johnstone Ritchie, had also been on the Supreme Court, serving as a puisne justice and then as the second Chief Justice of Canada.
His law practice was interrupted by World War II, where he served as Assistant Deputy Judge Advocate with the Third Canadian Division from 1941 to 1944. After the war he helped found the law firm, Daley, Phinney & Ritchie. He was a lecturer on insurance law at Dalhousie University, and acted as counsel to the royal commission on the terms of Newfoundland's union with Canada in 1949.
In 1959, without any previous judicial experience, Ritchie was appointed by the Diefenbaker government to replace Ivan Rand on the Supreme Court of Canada.
Ritchie's judgements were typically conservative, which often put him on side with Ronald Martland and Wilfred Judson. He is best known for a pair of conflicting decisions concerning the Canadian Bill of Rights: R. v. Drybones and Attorney General of Canada v. Lavell. In Drybones, Ritchie wrote the majority decision for the Court, holding that a provision of the Indian Act was inoperative because it conflicted with the Canadian Bill of Rights. However, in Lavell, Ritchie wrote the majority decision holding that a federal statute such as the Indian Act could not be held inoperative because of the Bill of Rights.