NEW YORK—A federal appeals court has revived a $1 billion lawsuit by Viacom Inc. against Google Inc.'s YouTube over alleged unauthorized posting of Viacom content.

Viacom had sued YouTube, claiming the website allowed users to post copyrighted Viacom content without permission between 2005 and 2008, including content from Comedy Central's "The Daily Show" and "The Colbert Report."

In...