This is the 33-year-old actor's first win and nomination for an Academy Award.
Benedict Cumberbatch ("The Imitation Game"), Bradley Cooper ("American Sniper"), and Steve Carell ("Foxcatcher") were also nominated.
In the biopic, Redmayne portrays Stephen Hawking as the young physicist is diagnosed with motor neuron disease.
Redmayne spent four months studying Hawking's life, and it paid off.
Hawking was so impressed with Redmayne's performance that he offered the filmmakers permission to use his trademarked computerized voice in the film.
Redmayne previously won the Golden Globe and BAFTA awards for best actor for his role in "The Theory of Everything."