The Oscar-winning actor is all too aware of the hefty responsibility that comes with such a role and immediately set about educating himself on the trans community, meeting with famous trans people including activist Paris Lees, his Jupiter Ascending director Lana Wachowski and former Vogue model April Ashley.
"People were so kind and generous with their experience, but also so open. Virtually all of the trans men and women I met would say, 'Ask me anything'. They know that need for cisgender people to be educated," Redmayne told Out magazine.
"I felt like, I'm being given this extraordinary experience of being able to play this woman, but with that comes this responsibility of not only educating myself but hopefully using that to educate [the audience]. Gosh it's delicate, and complicated."
Redmayne has a growing reputation for taking on challenging roles, after winning the Best Actor for his portrayal of Stephen Hawking in The Theory of Everything at the Oscars earlier this year.
The 33-year-old was critically-acclaimed for his brilliant portrayal of the physicist, who was diagnosed with motor neurone disease aged just 21. Even Hawking said that watching Redmayne play him in the movie was like watching himself.
Redmayne has already faced criticism for taking on the part of the first person to undergo gender reassignment surgery, which many believe should be played by a trans actor. Jared Leto received a similar backlash after winning Best Supporting Actor for his role as HIV-positive, drug-addicted trans woman Rayon in Dallas Buyers Club.
But when asked by Lees about Hollywood's tendency to cast cis actors in trans roles, he replied: "Look, I've just played a man in his fifties with motor neurone disease. I'm acting."
Lees has spoken out against poor trans representation in film before, including in an article for The Independent, but she gave her blessing to Redmayne after seeing how dedicated he was to understanding the role.
"I don't think that if and when they make a biopic of my life I would want a cisgender man playing me," she said. "Politically, it makes me groan. But if anybody's going to do this justice then I'm happy it's Eddie."
Trans issues have been hitting headlines recently, thanks in part to the high-profile likes of Orange is the New Black actress Laverne Cox and former Olympic athlete Caitlyn Jenner. Redmayne "salutes Jenner's courage" and was in New York when the Vanity Fair cover announcing her new identity came out.
Landmark LGBT TV moments
Landmark LGBT TV moments
1/9 EastEnders gay kiss - 1989
EastEnders becomes the first British soap to screen a kiss between two gay men. The Sun branded the landmark kiss between Colin and Guido as a “ love scene between yuppie poofs”.
2/9 Orange is the New Black – 2013
The Netflix series features lesbian and bisexual women of different colours and sizes, but its greatest accomplishment is the honest portrayal of its transgender character, Sophia Burset (played by Laverne Cox).
3/9 Brookside lesbian kiss - 1994
Brookside followed suit as the first to screen a lesbian kiss when Beth and Margaret shared a passionate embrace.
4/9 Lesbian lead on US TV - 1997
US TV gets its first ever lesbian lead, as Ellen Morgan (played by Ellen DeGeneres) came out in a special two-part episode of ABC's Ellen.
5/9 Primetime TV gets gay characters - 1998
Will & Grace debuts on NBC as one of the first primetime US series to feature lead gay characters. Actors Eric McCormack and Sean Hayes played Will and Jack on the successful show that ran for eight seasons.
6/9 First lesbian drama series - 2004
Television gets its first predominantly lesbian dramatic series in Showtime's The L Word.
7/9 Glee - 2009
Glee is the television show with the most number of regular and recurring homosexual characters, according to the Gay & Lesbian Alliance Against Defamation (GLAAD). Glee has won four Golden Globes, including a supporting actor nod for Chris Colfer—who played bullied open gay character Kurt Hummel.
8/9 Modern Family – 2009
The Emma-winning and progressive ABC series features an interracial and extended family along with leading gay characters Cam and Mitchell as the adored married couple.
9/9 E4's Cucumber, Banana and Tofu – 2015
Russell T Davies' recent trio of programmes bring a sensitive and serious yet funny portrayal of contemporary queer life with gay and lesbian lead characters—Henry and Scotty.
Directed by Tom Hooper (The King's Speech, Les Miserables), The Danish Girl is not due in UK cinemas until 1 January 2016.
It is of course impossible to judge Redmayne's performance until then, but he knows what he wants to do with the film, and that is to "hammer home to the world" that gender and sexuality are not always related, something he describes as his "greatest ignorance" when he started on the film.
"You can be gay or straight, trans man or woman, and those things are not necessarily aligned," he said. "[Gender] is fluid, and it needn't be labeled."