The 21-year-old had only just returned to Stamford Bridge following the conclusion of a similar deal with Wigan Athletic.
"We have shopped around and the preference was for a left-footed player," said Vitesse manager John van den Brom.
"The moment the name of Patrick came up, everyone was immediately enthusiastic.
"He is a talented young player who wants to show himself at the highest level and the advantage is that he is fit and is ready to play."
Aanholt has had previous loan spells with Coventry City, Newcastle United and Leicester City.