The Oscar-winning actor's wife Hannah (nee Bagshawe) gave birth to a baby girl named Iris Mary Redmayne on 15 June.
A rep for the star confirmed the arrival to Daily Mail, saying: 'I can confirm that Eddie and Hannah Redmayne have welcomed their first child."
No further details were given.
A birth announcement was also printed in The Times newspaper.
Hannah was a familiar face during last year's awards season, accompanying Eddie to a string of high profile events, including the Academy Awards, where he picked up 'Best Actor' for his role as Professor Stephen Hawking in The Theory of Everything.
Eddie and Hannah announced the pregnancy back in January, and Eddie publicly stated they wouldn't be learning their child's sex ahead of the birth, calling it one of life's big surprises.
The couple met as teenagers, while Eddie was attended the exclusive Eton school and Hannah attended a school nearby. Boys from Eton were invited to Hannah's school to take part in a charity fashion show.
Eddie previously told Daily Mail: "I saw Hannah across the room at a party afterwards and she was very beautiful and very funny and she loves the arts and theatre just as I do, so we became friends.'"
Romance blossomed twelve years later, with Eddie recounting: "I'd finished rehearsals [for Les Miserables] and was about to start shooting in a few days and so I said to myself, 'I'm going to go to Florence for a quick break and write or do something like that.'
"Before I went, Hannah and I were on a sort of date — we'd been good friends for 12 years — and we had a wonderful evening and I suddenly said, "You don't want to come to Florence with me next week, do you?" She said, "That's absurd, you don't mean it." I said, "Yes I do!" So our first proper date was in Florence. That was three years ago and we couldn't be happier."
Congrats to Eddie and Hannah!
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