The positive tests were taken in connection with a tournament in Spain in June, and the 31-year-old Kyrgios has been suspended since early August pending further investigation.
According to tennis' anti-corruption and doping body ITIA, Kyrgios has admitted taking cocaine in connection with a night out in the resort of Magaluf in Mallorca.
According to AP, the anti-doping organisation Wada's standard period for a suspension of this type - three months - can be reduced to one month provided that the athlete undergoes treatment, which Kyrgios now chooses to do.
He has previously described the incident on social media as "a big mistake."
Both prize money and ranking points from the Spanish tournament will be taken away from the Australian.
