Barron will leave the business in March. A successor is likely to be recruited internally.
He first joined the firm as UK, Ireland and Benelux comms director in 2008. Before that he was a BBC Newsnight editor, and previously worked for ITV and Channel 4 News.
Barron confirmed the news of his departure, first reported by BBC journalist Amol Rajan on Twitter, to PRWeek.
He told Google colleagues in an email yesterday: "I want to say thank-you to every one of you for the truly wonderful and unexpected experience I've had at Google. It has been an immense privilege to work with you over the years. You are the most talented and committed team I've ever worked with and I know you'll continue to thrive.
"Having spent the last week with Sundar [Pichai, Google's CEO] and the other leaders in Davos I also feel great optimism both about Google's future and about the positive role of technology more generally - despite all the obvious challenges. I know that as a team you are very well set for the campaign ahead."
He will be taking time out to convert a barn in Spain, Barron said.
During his time at Google, Barron has had to defend the firm against criticism of its tax affairs on several occasions, and latterly has been a spokesperson on the issue of brand safety, with terrorist and other illicit content appearing on YouTube, which is part of Google.
Google's EMEA president Matt Brittin said: "Peter has been an inspiring and valued colleague, friend and leader who is highly regarded both inside and outside Google. He has been an important part of all the big moments for Google in the last ten years. We will miss him and we wish him all best in his next endeavours."