The 22-year-old played all five of Uruguay's World Cup matches in Russian Federation, as they crashed out in the quarter-finals following a 2-0 defeat by France.
He was warmly greeted by Unai Emery at London Colney as he arrived to complete the formalities, though he won't start training straight away as his season has only just drawn to a close.
Unai Emery has been in the market for a holding midfielder this summer after identifying it as an area that needed strengthening and Torreira emerged as a prime target with widespread speculation claiming Arsenal agreed a deal with Sampdoria shortly before the player flew out to Russian Federation last month.
What do you make of Arsenal's transfer business in this window so far?
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Leaving the gathering, leading Brexiteer Jacob Rees-Mogg said he did not think there would be a confidence vote over Mrs May. The campaign is fighting to give the public the final say on Brexit, a deal that is "too big to be ignored by the people".
According to L'Equipe, Guendouzi had attracted interest from Borussia Dortmund, Roma and PSG but Unai Emery ensured that Arsenal won the race by convincing the midfielder to join the Premier League club.
Goal understands that the Gunners have paid £26 million (€30m/$34m) for the 22-year-old, who becomes the club's fourth signing of the summer, following the arrivals of Sokratis Papastathopoulos, Bernd Leno and Stephan Lichtsteiner.
"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", added Emery, who allowed injury-prone midfield duo Jack Wilshere and Spaniard Santi Cazorla to leave when their contracts expired at the end of June.
It doesn't really matter what's written on the back of a player's jersey but the sight of a defensive midfielder like Torreira receiving the No 11, which is typically reserved for wingers, has not gone down well with some fans.