The 26-year-old spent the second half of the 2021/2022 season on loan with the Magpies from Villa Park, making 16 appearances in the top flight.
Targett helped Newcastle United claw away from the relegation zone after joining and they eventually finished 11th.
Newcastle manager Eddie Howe has now moved swifly to secure Targett's signature on a permanent deal, with the former England u-21 international signing a four-year contract.
"I'm absolutely delighted to sign a four-year contract with this club," Targett told the club's official website.
"For me, it was an easy decision to make the loan permanent after the welcome I had from my fellow players, the staff, the supporters and the owners, so I'm really happy to be here."
Howe added: "Matt had a fantastic impact after joining on loan in January and made a big contribution to some excellent team performances.
"He is a great lad and a top professional who undoubtedly makes us stronger, so I'm delighted he sees his future here."
