Sydney made his name in 1915 in the London stage hit Romance by Edward Sheldon, with American Broadway star Doris Keane. He also costarred with Keane in the 1920 silent film of the play.
The couple married in 1918. When Keane revived Romance in New York City in 1921, Sydney made his Broadway debut in his lead role.
Embracing the new art of movies, Sydney performed in more than 50 films, most memorably as Claudius in Laurence Olivier's 1948 film of Hamlet. He also appeared in classic films such as Treasure Island (1950), Ivanhoe (1952), and Around the World in Eighty Days (1956). Still, the focus of his career was always the stage, on both sides of the Atlantic.
Sydney divorced Keane in 1925. In 1929, he married actress Mary Ellis, and the couple moved to England. There he concentrated more on film than on theatre work. In the 1940s, he married English film actress Joyce Howard; they had three children.
A heavy smoker, Sydney died from pleurisy in 1968, aged 73.