Torreira arrives at the Emirates on a long-term deal for a fee in the region of £26million.
The transfer has gone through for a reported £27million following Torreira and Uruguay's exit from the World Cup.
Arsenal teased the announcement with a social media video before announcing the deal themselves on Monday.
Torreira, 22, played at the base of Sampdoria's midfield diamond last season and is expected to bring bite and defensive nous to Unai Emery's team.
The new signing has a tattoo featuring a lion on his arm and said the king of the jungle best represents him and his people: "It's true that a lion represents strength and the spirit we Uruguayans have inside".
Torreira, who has only won eight caps for his country, featured in every game as Oscar Tabarez's side reached the quarter-finals, where they were beaten 2-0 by semi-finalists France.
Arsenal have been waiting to seal the deal due to Torreira being at the World Cup in Russian Federation as part of the Uruguay squad.
"We welcome Lucas to Arsenal and look forward to him joining us soon for pre-season".
According to the same story, Emery's past working relationship with N'Zonzi could give Arsenal the upper hand in the race to sign the former Blackburn Rovers and Stoke City midfielder.
Torreira will wear the No 11 shirt that Mesut Özil occupied until this summer, with the German instead set to be wearing the No 10 shirt vacated by Jack Wilshere, now at West Ham.