The Les Miserables star proposed to his girlfriend of two years last weekend when the pair were on a romantic holiday, according to US Weekly.
"He had been planning on it for a while," a source told the American magazine.
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"They have a very relaxed and supportive relationship. They seemed to have always known they were going to spend the rest of their lives together."
A man of tradition, Eddie, 32, reportedly asked Hannah's father for permission before getting down on bended knee.
The actor and singer has also modelled for the Burberry fashion label and been named as one of Vanity Fair's best-dressed people. He is best known for co-starring as Marius Pontmercy in the 2012 film adaptation of the classic musical Les Miserables, starring alongside the likes of Hugh Jackman and Anne Hathaway.
Eddie Redmayne and his publicist love Hannah Bagshawe have been together two years
Since gaining Hollywood recognition he has landed himself a role in sci-fi film Jupiter Ascending, in which he appears opposite Channing Tatum and Mila Kunis.
He has also recently been filming for the Stephen Hawking biopic, Theory Of Everything, in which Eddie plays the brilliant and renowned theoretical physicist.
The movie tells the poignant and inspirational story of the scientist's love for his first wife Jane Wilde.
Eddie and financial publicist Hannah have been dating since January 2012.
They made their relationship official when they appeared together on the red carpet at the London premiere of Les Mis in December, that year.