In a statement he said: “We have lost a truly beautiful mind, an astonishing scientist and the funniest man I have ever had the pleasure to meet.
“My love and thoughts are with his extraordinary family.”
Redmayne won the Best Actor Oscar for his portrayal of the acclaimed physicist in The Theory of Everything.
He described meeting Hawking while researching the role as “one of the great moments of [his] life”.
A slew of tributes poured in for Hawking in the wake of his death, aged 76.
Fellow scientist Professor Brian Cox – who Hawking once ‘ran over’ in a Monty Python sketch – tweeted: “Sad to hear about Stephen Hawking. What a remarkable life. His contributions to science will be used as long as there are scientists, and there are many more scientists because of him.
“He spoke about the value and fragility of human life and civilisation and greatly enhanced both.”
British astronaut Tim Peake praised him for “inspiring generations” and said his “personality and genius will be sorely missed”.
Prime Minister Theresa May also paid tribute hailing him as “a brilliant and extraordinary mind – one of the great scientists of his generation”.
She said: “His courage, humour and determination to get the most from life was an inspiration. His legacy will not be forgotten.”
David Walliams, who teamed up with Hawking for a Little Britain sketch, led the celebrity tributes, thanking him for being a “great laugh”.
Amanda Holden, Piers Morgan and Katy Perry also offered their condolences on Twitter.