The Potters were unsuccessful in securing a work permit for the 21-year-old striker in November last year, but have decided to still sign the player and send him to the Netherlands as he cannot play in England yet.
Stoke chief executive Tony Scholes told the club's official website: "We were surprised and bitterly disappointed when our application for a work permit was rejected by the appeals panel – as were many other people in the game.
"It's still our view that Juan is a great talent and is a player that Mark Hughes would like to join our squad. We have therefore decided that we are going to reapply for a work permit at the earliest opportunity.
"We have signed Juan but he cannot play in this country, so we're loaning him out to Utrecht to allow him to not only develop his experience of playing in Europe but also to stay match sharp."
Agudelo, whose contract with MLS side New England Revolution expired last month, has made 17 appearances at senior international level for the United States.