Doherty, 26, admitted the offenses during a hearing at Thames Magistrates' Court in London. He was freed on bail until sentencing on Feb. 8.
Police said the charges stemmed from Doherty's arrest in east London on Dec. 4, one of a string of drug busts for the lead singer of the band Babyshambles.
Doherty also was arrested on Nov. 30 and charged with possession of cocaine and heroin. He pleaded guilty last week and was released on bail.
He was stopped by police on Saturday while driving through east London and again arrested on suspicion of possessing drugs. He was released on bail and ordered to return to a police station for questioning on Feb. 2.
Moss, 31, lost valuable modeling contracts with H&M, Burberry and Chanel after the Daily Mirror tabloid published pictures in September of her apparently using cocaine in a west London music studio where Doherty, then her boyfriend, was recording.
She later went into a rehabilitation clinic in Arizona and has since resumed her modeling career.