Born in Montreal, Ramsay began his acting career with a screen debut opposite Elias Koteas in the film Malarek, which was released in 1988. This marked the beginning of a professional partnership between Ramsay and Koteas, who went on to appear in two more films together, Hit Me in 1996 and Collateral Damage in 2002.
Ramsay's breakthrough role came when he was cast as Carlitos Paez in the biographical survival drama Alive, directed by Frank Marshall and based on the 1974 book Alive: The Story of the Andes Survivors by Piers Paul Read. The film tells the story of the Uruguayan rugby team that crashed into the Andes mountains, and Ramsay's performance as one of the survivors helped establish him as a leading man in Hollywood.
In 2011, Ramsay made his directorial debut with an adaptation of Hamlet, in which he also starred as the titular character and served as producer. The film premiered at the Vancouver Film Festival in 2012 and marked a significant milestone in Ramsay's career as a filmmaker.
More recently, Ramsay has appeared in a number of high-profile projects, including Behind the Candelabra, a biographical drama about the life of pianist Liberace, which was directed by Steven Soderbergh and starred Michael Douglas and Matt Damon. This marked the second time that Ramsay had worked with Soderbergh, following his appearance in the 1995 film noir series Fallen Angels, in which he starred alongside Peter Coyote and Brendan Fraser.