"This is another great piece of news for the club," said Rafael Benitez.
"Dirk had one year left on his contract and we were keen for him to stay. He is a player with great quality who has a big part to play in our future. We are delighted to have reached an agreement.
"To have announced new deals for Steven and Dirk on the same day shows how hard everyone is working and that we are moving forward quickly as a club. These are very positive messages and I am very happy."