The 20-year-old has been capped 17 times for his country, scoring twice, and has scored 14 goals in 64 MLS appearances for New England, Chivas USA and the New York Red Bulls.
He has signed a pre-agreement with Stoke, joining up with them when his contract expires on January 1. Agudelo will become the fourth US international at the Britannia Stadium, joining Geoff Cameron, Maurice Edu and Brek Shea.
"We've put a lot of work into this deal, and I am delighted that we have managed to get the deal over the line," Stoke manager Mark Hughes said on the club's website.
"It's a good deal for us, because he is a very good young player who boasts a lot of talent as well as a lot of potential too.
"I've known of him for a couple of years now. He burst on to the scene for the United States at the age of 17 and everybody has paid attention to him since."
(Reporting by Josh Reich)
