The 36-year-old, who was representing Northamptonshire, tested positive for a cocaine metabolite after undergoing an anti-doping test on T20 Blast Finals Day on July 18, when his side won the title.
Lynn was provisionally suspended on July 31 and later admitted using cocaine during a period spanning July 15 to 16.
The English cricket regulator accepted that the drug was used out of competition and was unrelated to sporting performance.
One of two anti-doping charges against Lynn was subsequently dropped after the level detected in his sample fell below the threshold required under World Anti-Doping Agency rules.
The regulator initially sought to impose a three-month ban, but reduced it to one month after Lynn committed to a substance abuse treatment programme that was completed on August 30.
Lynn, who represented Australia in four one-day internationals and 18 T20 matches, has not played professional cricket since the start of his suspension and has yet to sign with a Big Bash League team for the upcoming season.