The versatile 20-year-old, who came through the youth ranks at Fratton Park, will complete his move to Meadow Lane on 1 August upon the expiry of his Pompey contract.
Oxlade-Chamberlain, the brother of Liverpool and England midfielder Alex Oxlade-Chamberlain, featured against the Magpies in last season's FA Cup while on loan at Oxford City.
"I believe I caught the eye of the manager (Kevin Nolan) in the FA Cup," Oxlade-Chamberlain told the official club website. "He wants me to bring some competition in the right-back position.
"In the past I always played in central midfield or out wide. Last year was my first playing right back and I really enjoyed it because I like both sides of the game - one-on-one defending and being able to get forward.
"It took a little while to get my head around the idea of leaving Portsmouth but I think it's good for me to get out of my comfort zone and push myself. I want to try and get into the first team, then help the team go for promotion, which is what everyone should be aiming for."
Oxlade-Chamberlain has spent time at loan at a number of clubs including Eastbourne Borough, Salisbury and Poole Town.