The 'Careless Whisper' hitmaker intended to mount a legal challenge to his eight-week prison sentence for possessing cannabis and driving under the influence of drugs.
But his legal team withdrew its application just hours ahead of a scheduled appeal and bail hearing at a court in London on Friday, reported Contactmusic.
A court spokesperson said a letter from criminal defence firm Burton Copeland stated the 47-year-old singer was officially "abandoning the appeal".
Michael was jailed for eight weeks on Tuesday and hit with a USD 1,875 fine for crashing his Range Rover into a shopfront near his home in Hampstead, north London, in July while he was high on cannabis.
The singer is due to be released after serving half his sentence.