Pogba had been originally suspended for four years by Italy's national anti-doping tribunal (Nado) in February.
The former Manchester United said on Friday: "Finally the nightmare is over. I can look forward to the day when I can follow my dreams again.
"I always stated that I never knowingly breached World Anti-Doping Agency regulations when I took a nutritional supplement prescribed to me by a doctor, which does not affect or enhance the performance of male athletes.
"I play with integrity and, although I must accept that this is a strict liability offence, I want to place on record my thanks to the Court of Arbitration for Sport's judges who heard my explanation.
"This has been a hugely distressing period in my life because everything I have worked so hard for has been put on hold."
BBC Sport says Pogba can resume training with Juve in January and can resume playing in March.