Butler, 18, started the season with Grove but impressed against Hartlepool United in the FA Cup, so much so that the north east side then took him on loan.
He has struggled to break into the Hartlepool first team and now returns to the EVO-STIK League West Division club on an open work experience registration.
A club statement said: “The management team and board have been working around the clock to get this deal over the line as well as other signings made in recent weeks and are delighted to finally have their man.”
Stoke retain the option to recall Butler at any time.
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