The 27-year-old, who scored four goals in 34 games for Oldham last season, was released at the end of the campaign and has signed an undisclosed length short-term deal at Home Park.
He was Everton's youngest ever first-team player when he made his debut aged 16 at the start of the 2008-09 season.
Baxter twice failed drugs tests while at Sheffield United, but has since talked of how he has turned his life around following the birth of his daughter and the influence of Everton chairman Bill Kenwright.
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