The 19-year-old forward became the youngest player ever to play for the Toffees when he made his first-team debut in August 2008, although injuries and off-field problems have since interrupted his progress.
Baxter, who has represented England at Under-16 and Under-17 level, was named Everton's reserve player of the season last term and has made 14 first-team appearances to date.
Rovers manager Les Parry said: "I'm delighted to be able to bring Jose to the club.
"We watch Everton reserves a lot and he's tailor made for that role just behind the striker. He sees a pass, he can score a goal and he has great awareness.
"Plus he can tackle and put himself about, so he brings to us everything we're looking for."
Source: Team Talk
Source: Team Talk