Targett spent the second half of the season on loan with Newcastle as part of boss Eddie Howe’s revamp of the Premier League side.
The left-back made 16 appearances as Newcastle successfully fought to avoid relegation and eventually finished in mid-table.
Targett has now agreed a four-year contract with Newcastle, becoming the club’s first close-season transfer in a deal worth a reported £15 million ($18 million).
“I’m absolutely delighted to sign a four-year contract with this club,” Targett said.
“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.”
Impressed by Targett’s impact after his arrival, 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.”