Arismendi seals Stoke switch
The transfer fee for the 21-year-old - who has played twice for Uruguay having made his debut in a friendly against Norway in May last year - could rise to 5.5 million euros.
Arismendi's arrival on a four-year deal follows Stoke's double swoop for Germany defender Robert Huth and Turkey forward Tuncay from Championship Middlesbrough last week. Stoke are fifth in the table after a promising start.
"This is the first time the club has signed a player directly from South America," Stoke chief executive Tony Scholes told the club's website.
"Clearly, Diego will need time to settle in, but we are excited by his potential and are confident he will prove to be a great acquisition."
Arismendi helped Nacional win Uruguay's league title this year having featured 28 times and was Player of the Year.