The film had been doing the rounds in Hollywood for many years but then Matthew McConaughey became involved and Leto thought "if he's doing it, then there's something there... there's gold in the hills".
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The "gold" lay in the true story of electrician and hustler Ron Woodroof, who was diagnosed with Aids in 1985, and resolved to fight the system by smuggling unapproved pharmaceutical drugs into the US that improved his symptoms.
He also set up a buyers' club subsidised by membership fees to cope with demand among fellow sufferers and was able to prolong other people's lives by giving the drugs for free to subscribers.
Leto plays Rayon, a transsexual suffering from Aids, who becomes Woodroof's business partner and friend. But while the character is fictitious, Leto saw playing her as a chance "to put a real life on-screen rather than a campy cliché or stereotypical performance that I think we've seen quite a bit".
He won the role by meeting the film's director, Jean-Marc Vallee, via Skype.
"I was in Berlin, he was in the States. It wasn't an audition but it was kind of a test for both of us. We said hello and I reached out and put lipstick on and his jaw dropped. And then I undid my big coat and I had a little pink sweater underneath and I proceeded to flirt with him for the next 20 minutes. I woke up the next morning with the part."
With the role secured, Leto, 42, embarked on a gruelling physical transformation, losing 30lbs in three-and-a-half weeks, waxing his entire body and immersing himself in the character. Out went the rock star good looks synonymous with his duties as lead singer of Thirty Seconds To Mars, the rock band he co-created with his brother, and in came heels and tights, as well as sickness and sores.
"One day I was in the chair for eight hours... eight hours getting different stages of sickness put on," he adds.
He even stayed in character, although he baulks at the term "going method".
"I just think of it as another word for staying in character or staying focused and committed. There are no rules - you do what enables you to deliver the best performance possible.
"But what was great about it for me is that I really had the opportunity to work when I wasn't in front of the camera. The way people start treating you is fantastic because you learn so much from it. There would be an assistant director who reaches for your hand when you are walking down the stairs, or a grip who opens the door for you, or a carpenter who asks you out on a date. It means that you get to practice all the time."
It's worked well for critics too. Along with McConaughey's, Leto's performance is being hailed as one of the best of his career, which includes high-lights such as Requiem For A Dream, Fight Club and Lord of War. He has already won Golden Globe and Screen Actors' Guild Awards as best supporting actor and is hot favourite for a Bafta and an Oscar.
Leto himself remains modest, embracing the positive feedback but noting how lucky it is at the same time. Citing past experiences, he says: "Largely I've made smaller films, art-house films and independent films, and they can break your heart. They're difficult to get made, they're difficult once you've gotten financing to make them with the little bit of money you have, they're difficult to distribute, they're just a pain in the ass. But they can also change your life and in this case it worked. So, it's nice to celebrate the film and it's nice that people have been so enthusiastic."
Does that mean Leto is now going to concentrate more on acting than singing? "I don't know, I'm not thinking about it too much," he replies, before then being drawn on his passion for music and the similarities between the two careers.
Is it right he feels most true to himself performing with Thirty Seconds to Mars?
"In a lot of ways that's true. When you stand on the stage it can reveal a lot. There is no script, your life is the script and the songs are the dialogue," he says. "But when you build a character you have a sense of that going on too. You are inventing, you're pulling pieces of yourself and magnifying those. And when you dive that deep you fall in love. That's why I think this is always going to be an important time in my life."
Dallas Buyers Club opens in cinemas on February 7