Koch filed a federal lawsuit in 2007, accusing Greenberg, the San Francisco-based founder of several Internet companies, of fraud and misrepresentation and seeking $320,000, the amount he paid for the 24 bottles.
The jury on Thursday evening returned with a verdict that Koch should be compensated for the amount he spent on the wine, and on Friday the panel decided on the $12 million in punitive damages.
Koch shook hands with jurors and thanked them as they left the courtroom, saying he was "out of sight, over the moon" over the damages award.
Greenberg had denied the charges, saying any forgeries from his wine cellar got to the auction house by mistake.
Experts for both sides agreed that the wine in one of the 24 bottles is fake. The authenticity of the other 23 bottles was unclear, although expert witnesses testified that some of the labels were copies of the originals.
None of the bottles has been opened nor the wine tasted.
In closing arguments on Thursday, Greenberg's attorney Arthur Shartsis said his client did not knowingly sell fakes. He argued that the New York-based Zachys auction house sold the bottles "as is," meaning the buyer accepted the product in whatever condition it was at the time.
Greenberg's contract with the auction house did not require him to prove the wine was real, the attorney said.
Koch's lawyer John Hueston said in court that Greenberg withheld information about the provenance and authenticity of his wine collection.
Koch, whose brother David Koch is a major supporter of conservative political causes, settled a separate lawsuit with the auction house in 2011, details of which were kept private.