Baxter became a media consultant from the beginning of this month, but Bauer will continue to command much of his time as one of his launch clients.
Bauer Media will continue to be represented by Baxter on the boards of audience measurement system Rajar, the digital radio switchover organisation Digital Radio UK, and RadioCentre, the trade body for the commercial radio industry.
Baxter said: "I have been developing some really interesting new projects in private equity overseas, and in both the online and not-for-profit sectors in the UK. I am delighted I will be able to combine these with my work with Bauer Radio.
He added: "In particular, I will be able to work more closely in the content area, which was the thing that brought me into media in the first place, and which is now even more significantly the key to success in this fragmenting media landscape."
In autumn 2008, Baxter stepped down from the day-to-day operations of Bauer Media radio to focus on regulation, external affairs and strategy.
A major part of the role was to represent Bauer in the Digital Britain review and the subsequent Digital Economy Bill, which became law last week.
Dee Ford, group managing director of radio at Bauer Media, said Baxter had played "a significant role" in developing the business and said he would continue to "deliver great results" in content development and external affairs.
Baxter joined Bauer Media, then Emap, as managing director of local radio in 2004, and became managing director responsible for strategy in 2008.
Prior to joining Bauer, he worked for the private equity firm Advent International.
Baxter has more than 30 years of experience in broadcasting, including 10 years as a regional managing director of RTL Group. He started as a producer on local radio at the BBC.