NAC Breda had been keen to sign Cornelisse which would have reunited him with his brother Yuri, but Utrecht have proved to be the most persuasive.
Vitesse had little option but to allow Cornelisse to move on as he was one of their highest-paid players and their dire financial plight meant they had to cut costs.
The 26-year-old, who has moved for a small fee, has inked a four-year deal.
He still has unfinished business with Vitesse, as he will not move to Utrecht until the Eredivisie play-offs are finished.
Vitesse have to win their play-off group in order to preserve their status and Cornelisse is likely to play a key part.
