For a number of weeks, Arsenal have been heavily linked with the player, but a deal has been held up due to Uruguay reaching the World Cup quarter-finals.
However, four days on from their exit from the competition, Arsenal are now in a position to announce the arrival of the 22-year-old for an undisclosed fee.
Manager Unai Emery told the club's official website: "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."
Torreira will not link up with Arsenal until next month following a period of rest after the World Cup.