Regulators in the U.S. and European Union are investigating Google Inc. for bypassing the privacy settings of millions of users of Apple Inc.'s Safari Web browser, according to people familiar with the investigations. Google stopped the practice last month after being contacted by The Wall Street Journal.

The investigations—which span U.S. federal and state agencies, as well as a pan-European effort led by France—could embroil Google in years of legal battles and result in hefty fines for privacy violations. The Journal in...