Lilly made the announcement via a statement to the Windy City Media Group, in which she confirmed that she has transitioned and is out to her friends, family and some coworkers.
Wachoski's sister, Lana, first appeared publicly as a woman in July 2012. The siblings are best known for directing The Matrix trilogy.
In her statement, Lilly says she was nearly outed by the media several times over the past year. "In response to this threatened public outing against my will, I had a prepared a statement that was one part piss, one part vinegar and 12 parts gasoline," she writes.
Lilly says a reporter from The Daily Mail approached her at her home on Monday night and pressured her into giving the paper an exclusive on her transition.
Citing the controversy over a Daily Mail columnist's criticism of a a transgender schoolteacher named Lucy Meadows who later committed suicide, Wachowski wrote: "And now here they were, at my front door, almost as if to say – 'There’s another one! Let's drag 'em out in the open so we can all have a look!' "
The Mail in a statement told PEOPLE: "DailyMail.com categorically denies that it in anyway tried to coerce Lilly Wachowski into revealing her gender transition... we made absolutely clear at several points in the conversation that we were only interested in reporting the story if and when she was happy for us to do so and with her cooperation."
The Mail also denied playing a party in the suicide of the British teacher, saying that an investigation into her death found no mention of media coverage in her suicide note.
Lilly says she still feels lucky "having the support of my family and the means to afford doctors and therapists has given me the chance to actually survive this process." She also notes that those who do not have support often fall victim to the staggering high rates of murder and suicide plaguing the trans community.
"My sister Lana and I have largely avoided the press. I find talking about my art frustratingly tedious and talking about myself a wholly mortifying experience. I knew at some point I would have to come out publicly. You know, when you're living as an out transgender person it's … kind of difficult to hide. I just wanted – needed some time to get my head right, to feel comfortable," she writes. "But apparently I don't get to decide this."
She adds: "So yeah, I’m transgender. And yeah, I’ve transitioned."
Eddie Redmayne on Conversation Surrounding Trans Community: 'It's a Civil Rights Movement'
Lilly also added that she feels the words "transgender" and "transitioned" have "lost their complexity in their assimilation to the mainstream," explaining that, "my reality is that I've been transitioning and will continue to transition all of my life, through the infinite that exists between male and female as it does in the infinite between the binary of zero and one. We need to elevate the dialogue beyond the simplicity of binary. Binary is a false idol."
GLAAD director of programs for transgender media Nick Adams issued a statement to PEOPLE celebrating the news and cautioning the media in its coverage: "GLAAD is thrilled that Lilly Wachowski is able to be her true and authentic self today, however, she should not have been forced to disclose her transgender identity before she was ready to do so. Journalists must learn that it is unacceptable to out a transgender person, in the same way it is unacceptable to out a person who is gay, lesbian, or bisexual."