Baxter, 23, has made 10 appearances for Town this season, scoring two goals. The last of which came against his new club in a 3-1 defeat.
His other goal came in a 2-1 win over Bootle Town last month.
In a tweet, the club said: “Following a 7 day approach we have successfully signed forward Ryan Baxter from Newcastle Town.
“Ryan scored against the Albion a couple of weeks ago but has now decided to join Jon Macken's forever improving squad.”
Albion currently lie in sixth place, just three points behind Clitheroe, who currently occupy the final play-off place.
Baxter could make his debut on Saturday, as Witton host Prescot Cables.
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