De Jong, who spent the second half of last season on loan at the Magpies, and has not scored a competitive goal in over a year, returns to the Netherlands, where he was the Eredivisie's second-highest goalscorer in 2011-12 with 25 for FC Twente.
"Eindhoven desperately wanted to sign Luuk and we were able to reach an agreement on terms," said Gladbach's director of sport Max Eberl.
"We wish Luuk all the best for his future and we look forward to seeing him again in a friendly game that we've arranged."
De Jong scored only eight goals in 44 games for the Foals, whom he joined in 2012 from Twente for a club-record fee of around 12million euros (£9.5m).
He could face his former club in the Europa League next season with both PSV and Gladbach having qualified for the competition.