The star, lauded for his performance as Professor Stephen Hawking in The Theory Of Everything, saw off competition from big names including Bradley Cooper and his friend – and fellow Brit –.
Accepting his award from Cate Blanchett, a shocked Redmayne said: "I don't think I'm capable of articulating quite how I feel right now. I'm fully aware that I'm a lucky, lucky man".
He dedicated the award to "all of those people around the world battling" motor neurone disease – the illness that left Professor Hawking in a wheelchair.
Eddie Redmayne was shocked to win the 2015 Best Actor Oscar (Reuters)
Clutching his Oscar, Redmayne said: "I will be its custodian and I promise you I will look after him, I will polish him, I will answer his beck and call and wait on him hand and foot " and thanked the Hawking family and his wife, Hannah.
Redmayne, who has also won a Golden Globe, Bafta and Screen Actors Guild for the performance, also thanked his "staggering partner in crime Felicity Jones" who lost out on the leading actress Oscar to Julianne Moore.
