The jury verdict, issued in the US District Court for the Eastern District of Texas, found that Google had infringed the four patents through its Chrome browser.
The case was originally brought in 2013, by Alfonso Cioffi and the children of his co-inventor, Al Rozman.
In December 2014, the court dismissed the case after the plaintiffs conceded that they would not win on the court's interpretation of the asserted patent claims.
The plaintiffs took their appeal to the Federal Circuit, which found that the court had erred in its interpretation.
Google asked the US Supreme Court to hear the case, but it declined.