His father, the Reverend Featherstone Lake Osler (1805–1895), the son of a shipowner at Falmouth, Cornwall, was a former lieutenant in the Royal Navy and served on H.M.S.

Beagle as the science officer on Charles Darwin's historic voyage to the Galápagos Islands, but he turned it down as his father was dying.

On arriving in Canada, he and his bride (Ellen Free Pickton) were nearly ship-wrecked again on Egg Island in the Gulf of Saint Lawrence.

Osler first rose to national prominence by helping to secure the conviction of Louis Riel on charges of treason following the North-West Rebellion of 1885.

He subsequently represented the government of Canada in arbitrations with the Canadian Pacific Railway arising from construction contracts carried out by contractor Andrew Onderdonk.