The Greece international has joined Sevilla on a season-long loan.
Vlachodimos made one appearance for the Magpies last season - as a substitute in October's Carabao Cup victory over AFC Wimbledon - following his summer switch from Nottingham Forest.
He told Sevilla FC+: “I`m happy to be here. It was like a rollercoaster ride of waiting. I couldn`t wait to come and finally we made it, I`m very happy to be here and I`m looking forward to meeting my teammates, the staff and the coaching team and I can`t wait to get started.
"I started in Stuttgart at a very young age, going through all the youth teams until I reached the first team. Then came the opportunity to go to Panathinaikos to play there and enjoy some great derbies. I think I developed as a goalkeeper. The next step was then Benfica, where I also took my first steps in international football. I started playing for the Greek national team then.
"Then, after five years in which Benfica won many titles, everything was ready for the next step. I felt ready for the Premier League, so I went to Nottingham Forest, where I spent more than a year, and then I moved again to Newcastle, and now I`m here."