The 33-year-old won for his role as theoretical physicist Stephen Hawking in "The Theory of Everything", the world's most famous living scientist crippled by an advanced form of motor neurone disease.
He had already scooped a Golden Globe and is hoping to add an Oscar later this month to complete the trio.
Among his fellow Oscar nominees was his friend and fellow British thespian Benedict Cumberbatch, who also played a troubled genius, Alan Turing, in "The Imitation Game".
Redmayne has won plaudits for his theatre work over the past decade, and has had parts in a number of major films, but this was his first leading man role -- and it has propelled him into the big league.
The film tells the story of Hawking and his wife Jane, starting in the 1960s at Cambridge University -- before he was diagnosed at the age of 21 with amyotrophic lateral sclerosis (ALS).
Based on a memoir by Jane, played by fellow Oscar nominee Felicity Jones, it charts how their relationship changed as his health declined and his fame grew, until their marriage fell apart in the early 1990s.
Redmayne was not the first choice to play Hawking. But he managed to arrange a meeting in a pub with director James Marsh, where he drank too much beer out of nerves and secured the part without an audition.
Immersing himself in the role, he spent four months visiting people with motor neurone disease at a clinic in London and reading everything he could by Hawking.
The result is a physical transformation that has been compared to Daniel Day-Lewis's Oscar-winning performance in "My Left Foot".
Hawking has reportedly said there were moments watching the film when he thought he was watching himself, and he gave the ultimate seal of approval by allowing the director to use his trademark computerised voice.
Redmayne said he was "terrified" that Hawking might not like it, but that it was an honour to spend time with him -- even if the first meeting started badly.
Lost for words, the star-struck actor blurted out that they were both Capricorns, to which Hawking replied: "I'm an astronomer, not an astrologer."
The son of a London banker with four siblings, Redmayne took acting classes from a young age and was a child extra in the West End production of "Oliver!".
He attended the elite Eton school alongside Prince William and studied History of Art at Cambridge -- the same university where Hawking still works.
Barely a year after graduating, Redmayne had a part in an all-male production of "Twelfth Night" by Shakespeare's Globe theatre, and by 2004 had won his first theatre award.
A few years later he picked up both a Laurence Olivier award and a Tony award for his role as artist Mark Rothko's fictional assistant Ken in the play "Red".
He has also appeared in a number of hit films including "The Good Shepherd", "Elizabeth: The Golden Age" and "The Other Boleyn Girl". He also played Marius in the Oscar-winning 2012 musical "Les Miserables".
Like Cumberbatch, Redmayne is blessed with chiselled good looks that always had the potential to make him a star, and has modelled for luxury brand Burberry.
Both men have a legion of fans on Twitter, dubbed respectively the "Redmayniacs" and the "Cumberbitches", undaunted by Redmayne's recent marriage and Cumberbatch's impending nuptials.
While the Hawking biopic has won him an Oscar nomination, the next film on his CV is set to send Redmayne's profile stratospheric.
Next month will see the release of the latest offering by "The Matrix" trilogy's Andy and Lana Wachowski, the sci-fi movie "Jupiter Ascending", in which Redmayne plays a villain with a six-pack.
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