The revelation comes just days after the former Brisbane and Adelaide BBL big-hitter was linked with a move to the Melbourne Renegades for the season, which begins next month.
The 36-year-old was handed the suspension in August, after he tested positive on the day of England's T20 Blast finals in July, having helped Northamptonshire to the title.
After tests revealed an adverse analytical finding for cocaine's metabolite benzoylecgonine, Lynn admitted to using the drug days earlier.
The findings noted Lynn did not have a therapeutic use exemption for cocaine and that the cricketer had successfully argued his drug use amounted to an out-of-competition violation unrelated to sporting performance.
He was given a one-month ban, backdated to the period of between July 31 and August 30.
Lynn was set to play in Sri Lanka after the T20 Blast, but after one appearance he was ruled out with an unspecified leg injury on July 29.
Any further punishment would be at his BBL club's discretion, with Lynn available given he has served his penalty and not on a Cricket Australia contract.
Lynn is the BBL's leading run-scorer and six-hitter, and has also played four one-day internationals and 18 T20 internationals for Australia.
He has also played for at least 25 different T20 franchises around the globe.
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