The She's in Parties singer was arrested for his part in a hit-and-run accident in Glendale, California in March (13), when police reportedly found methamphetamine inside the patrol car in which Murphy was detained.
The goth rocker previously pleaded not guilty to three charges, but in a Los Angeles court, he agreed to change his plea after striking a deal with prosecutors, who agreed to drop a misdemeanour charge of driving under the influence of drugs in return.
Murphy's drug charge will be axed and completely removed from his criminal record if he successfully completes 45 days of Narcotics Anonymous meetings. He also agreed to three random drug tests.
Murphy, who lives in Turkey, was ordered to return to court in May (14) to prove he has completed the programme.
He must also complete 10 days of community service for the hit-and-run charge.
Murphy is currently touring to celebrate the 35th anniversary of Bauhaus.