Torreira played a part in all of Uruguay's World Cup matches and started their quarterfinal defeat to France last Friday.
"A midfielder with great quality, I have enjoyed watching his performances for Sampdoria in the past two seasons, and we all saw him do very well for Uruguay in the World Cup," Emery said.
Torreira follows Stephan Lichtsteiner, Bernd Leno, and Sokratis Papastathopoulos this offseason to the north London club.