Kyrgios has been suspended after failing a drugs test on June 22 at an ATP 250 tournament in Mallorca, Spain.
The 31-year-old faces a ban ranging from a baseline three-month period to up to four years, if found to have used the drug in competition.
Kyrgios has been provisionally suspended since August 4.
The International Tennis Integrity Agency (ITIA) says Kyrgios, whose career world ranking peaked at No.13, could appeal against the provisional suspension but had yet to do so.
"I recently failed a drug test in Mallorca after testing positive for cocaine," Kyrgios posted on Instagram.
"I made a huge mistake and I take full responsibility for it.
"I'm sorry to my fans, my family, my sponsors and everyone close to me. Above all, I'm sorry to the kids who follow me. I know the example this sets and I'm deeply disappointed in myself."
Kyrgios, who played only four official singles matches on the elite ATP Tour this year, has battled knee and wrist injuries in recent years.
"I'm not going to make excuses, but I do want to give some context about where I've been," he wrote.
"The last couple of years of injuries have taken a huge toll on me, both physically and mentally.
"My body hasn't been able to do what my mind expects it to do, and coming to terms with being near the end of my career has been harder than I ever imagined."
But the polarising Canberra-born drawcard said that didn't excuse his actions.
"I've always said I didn't choose tennis - tennis chose me," he wrote.
"But letting go of something that has been my whole life is one of the hardest things I've ever had to face. At times I've felt helpless and alone.
"None of that excuses what I did."
Kyrgios said "the good news is that this has given me a wake up call.
"For the next 28 days, I'll be stepping away from social media and public life while I focus on getting myself right.
"I'd ask that people respect my privacy during that time, and most importantly the privacy of my family.
"I'm sorry. I'll do the work and come back better."
The ITIA said Kyrgios was suspensed for a ‌positive test for benzoylecgonine, a cocaine metabolite.
A World Anti-Doping Agency laboratory confirmed the positive result on July 17.
The former Wimbledon finalist is banned from playing, coaching or attending any tournaments sanctioned by the men's and women's tennis tours worldwide and national-level events in Australia.
Kyrgios last played in the men's doubles at Wimbledon in London on July 2, when he and partner Alexander Bublik lost in the first round.
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