The 22-year-old made 31 league appearances for Vitesse last term as they finished fourth in the Dutch top flight, securing Europa League qualification in the process.
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A statement on Vitesse's official website read: "Patrick van Aanholt will play again next season at Vitesse.
"The 22-year-old defender is hired for a season from Chelsea Football Club. Van Aanholt begins his third season in Arnhem."
The move follows Chelsea's capture of Vitesse midfielder Marco van Ginkel, who signed a five-year deal at Stamford Bridge on Friday.
Van Aanholt was part of the Netherlands squad for the Under-21 European Championship in Israel, and played in a 3-0 group stage loss against eventual winners Spain.