The New England Revolution striker has signed a pre-contract and will link up with compatriots Brek Shea, Maurice Edu and Geoff Cameron at City.
Manager Mark Hughes said: "We've put a lot of work into this deal, and I am delighted that we have managed to get it over the line.
"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.
"I have kept my eye on him for the last 18 months, and thankfully we were in a position where we were able to pull this deal off."
Agudelo, who has previously played for New York Red Bulls and Chivas USA, made his mark on the international stage with a goal on his debut against South Africa in 2010 and now has 17 caps.
He only joined the Revolution this year in what is his fourth season in Major League Soccer.
Stoke chief executive Tony Scholes believes the move underlines the growing strength of the American competition.
He said: "We've played against five MLS teams in the last two years and have been consistently impressed with the quality we've come up against.
"We've already taken two players directly from the MLS in Geoff and Brek.
"Geoff readily adapted to life in the Premier League by making 35 league appearances for us in his first season at the Britannia Stadium.
"Brek and Maurice will be looking to do likewise this season and we're confident that Juan will be able to follow suit."