Redmayne beat his fellow British actors Benedict Cumberbatch and David Oyelowo in a category dominated by biopics.
In The Imitation Game, Cumberbatch portrays Alan Turing, the computing pioneer who broke the Enigma code during World War Two, but was later persecuted by the British authorities for his homosexuality.
In Selma, a drama depicting the 1965 voting rights marches in Alabama, Oyelowo plays the celebrated US civil rights leader Martin Luther King, Jr.
Redmayne described the experience of making the film as a “huge privilege”, saying: “The Hawking family allowed us into their lives and they trusted us with their story. And getting to spend time with Stephen Hawking, who, despite all of the obstacles put in his way has lived passionately and fully and with great humour, was one of the great honours of my life.”
All three British actors are hotly tipped for Oscar nominations when the Academy unveils its own awards shortlists later this week.
Michael Keaton, who took home the Golden Globe for Best Actor in a Comedy or Musical, for his performance in Birdman, is also favoured to feature in the Best Actor category at the Oscars.
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