The owner of the Times of India bought Absolute Radio from STV in 2008 for £53.2 million when it was known as Virgin Radio. The station relaunched as Absolute Radio in September 2008.
Paul Keenan, the chief executive of Bauer Media UK, said, "We are looking forward to working with the award-winning team at Absolute Radio and have great respect for what it has achieved.
"We are excited about welcoming this complementary music radio business with renowned digital assets into Bauer."
Donnach O'Driscoll, the chief executive of Absolute Radio, said: "The Absolute Radio business has never been in better shape as we approach our fifth birthday.
"Bauer Media UK is a business that really cares about building famous media and entertainment brands and music radio in particular. This brand will continue to thrive as part of the Bauer group."