The 25-year-old Ghana international spent last season on loan at St. James' Park, making 32 league appearances and scoring five goals as Rafa Benítez's side lifted the Sky Bet Championship title.
The Magpies have now exercised an option to sign him for an undisclosed fee and the winger has penned a four-year deal.
The transfer is subject to Atsu successfully reapplying for a work permit.
Manager Benítez said: "We are happy to sign a good player.
"He's shown us that he's a good professional and someone who is very keen to learn and improve.
"Christian has been a key part of our promotion campaign and he wants to help us to build something for the future."