The Borussia Monchengladbach striker joined the Magpies on loan in January, but did not score during his 12 appearances for the team, resulting in the club not taking up an option to buy the 23-year-old.
The Dutch international told the club's website: "It hurts that I didn't score. Of course, I want to score goals. I'm a striker, and it's what I've done at every other club I have played for.
"I didn't score goals, and that's what I should do as a striker, so I''m not happy with that. I really enjoyed my time here, I like the club, the people who work here, the fans and the city. It's a great place to play football."
De Jong joined the Bundesliga side from FC Twente in 2012.