He moved to Atletico in 2014 and made 16 appearances for the La Liga giants last term.
Newcastle boss Rafa Benitez said: “I am really pleased to bring Jesus here to Newcastle.
“He is a very good defender who can play on both sides, left and right.
“He is experienced, I know he has great character and, importantly, he is an excellent professional. I am sure he will give balance to the team.”