Torreira, 22, completed his medical at Arsenal’s London Colney training base on Tuesday before the club announced the deal for an undisclosed fee.
Speaking to Arsenal website, Unai Emery said: “In Lucas Torreira, we have signed a young player who is a very bright talent in the game.
“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.
“He is a young player already with good experience, but who wants to keep on growing. We welcome Lucas to Arsenal and look forward to him joining us soon for pre-season.”
The Uruguay midfielder, who featured in all five of their games at the World Cup, will be given a break before joining up with the rest of his new team-mates in early August.