The 20-year-old, who has made just one first-team appearance for Pompey, will complete the transfer on 1 August.
Oxlade-Chamberlain, brother of England international Alex, featured against the Magpies in last season's FA Cup while on loan to Oxford City.
"I believe I caught the eye of the manager in the FA Cup," he said.
"Kevin [Nolan] wants me to bring some competition in the right-back position."
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