Farren began his career in the Showtime tele-movie, The Outsider, starring Naomi Watts and Tim Daly, in 2001, followed by a guest role in the Australian live action series, The Sleepover Club in 2002. He worked with several theatre companies in Australia, particularly the Sydney Theatre Company, the Griffin Theatre Company and the Belvoir Street Theatre. In 2007, he was cast as Cpl. John Powell in the well-received HBO mini-series, The Pacific, earning a reputation for intense performances.

Farren was born in north Queensland and raised in the Gold Coast from the age of six. "We had really great beach parties," Farren once said of growing up in The Gold Coast. "We'd enjoy ourselves all night by the water with music. They're the best parties I've ever been to." Farren once stated in an interview he always knew he wanted to be an actor: "I can't remember a time when I didn't watch a movie and think, 'That's what I want to do'... Growing up, people said you have to have a plan B. I never felt that, I always thought, nah, this is what I'm going to do." He attended Benowa State High School and studied in its French Immersion Program where students study typical subjects but receive at least half of their schooling in French. Farren graduated from the National Institute of Dramatic Art (NIDA) in 2007. He credits actors Daniel Day-Lewis and Gary Oldman as his primary influences and inspiration.

Farren worked his way through all the visual arts in 2008, starring in The Man In The Attic with the Sydney Theatre Co., the film Lucky Country, and the Seven Network television series, All Saints. In 2012, he earned a starring role in Jennifer Lynch's film, Chained, playing "Rabbit", a boy enslaved and raised by a serial killer played by Vincent D'Onofrio. Farren said, "... Shooting the film felt like second nature, the scenes would be focused but loose, incredibly tense but hilarious.I never had to say too much to her [Lynch], she would give me a look or whisper one word and I'd get it."

Farren's theatre career continued in 2014 with critically acclaimed roles as "Edward Ridgeway" in Switzerland and "Elliott" in Girl Asleep, which would be adapted to film and star Farren as a different character, "Adam/Benoit Tremet", a year later.

Farren starred as "Kirill" in Sydney Theatre Co's The Present in 2015, reprising the role in 2017 for its Broadway production which also starred Cate Blanchett in her Broadway debut.

Farren was cast as the character "Richard Horne" in the revival of the U.S. TV series, Twin Peaks airing in 2017.