CAS upheld Veerpalu's appeal against the ban imposed by the International Ski Federation after he tested positive for a banned growth hormone in January 2011.
Veerpalu, the 15km champion at the 2002 Salt Lake City Games and the 2006 Turin Olympics, retired soon after the positive test and it is unclear whether the 42-year-old would now plan a return to the sport.
"The panel notes that there are many factors in this case which tend to indicate that the athlete did in fact himself administer exogenous hGH (human growth hormone)," CAS said in its ruling.
"But that for the reason that the decision limits have not been proven as reliable in the course of this proceeding, the violation of the FIS ADR (Anti-Doping Rules) cannot be upheld on appeal.
"Therefore, the ban imposed by the decision of the FIS Doping Panel is overturned."
Veerpalu, who lost an appeal against the FIS in August 2011, has denied taking any banned substances.
- Sports & Recreation
- Addiction & Substance Abuse
- International Ski Federation