The Premier League club announced last August that the 21-year-old had signed a pre-contract agreement to join from the New England Revolution at the start of 2014.
However, Stoke were unsuccessful in getting a work permit for Agudelo in November, a decision that left chief executive Tony Scholes "amazed".
A brief statement on the club's official website on Saturday read: "Stoke City can confirm the club has been unsuccessful in its attempt to secure a work permit for Juan Agudelo.
"It is the second time the club have had an application for a work permit for the 21-year-old US international rejected by an appeals panel."
Agudelo has scored three goals in 14 Eredivisie appearances for Utrecht this season.
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