A move for Torreira had been placed on the back burner whilst the Uruguay worldwide was at the World Cup but, following La Celeste's elimination at the quarter-final stage, Arsenal moved quickly to wrap up his signing.
Torreira figures to replace Jack Wilshere who chose not to re-sign with his boyhood club after his contract expired, and instead joined West Ham on Monday.
Some Arsenal fans have reacted to the news that he will wear the No 11 vacated by Mesut Ozil - who has taken the No 10 shirt - with a mixed response, but it should be the least of their concerns.
Torreira claimed that he is looking forward to his new "adventure" in England.
The highly-mobile defensive midfielder set the Emirates side cost Arsenal a reported fee £27m and follows the trio of Stephan Lichtsteiner, Bernd Leno and Sokratis Papastathopoulos who earlier completed a switch the north London side this summer.
The combative midfielder reflected on the experience, saying: "I feel very proud of it, it all turned out great for me".
Speaking after his move was completed, Torreira said: 'I want to make the most of this opportunity life has given me.
Press Association Sport understands that Arsenal are also close to completing a deal to land France Under-20 worldwide Matteo Guendouzi.
The same article states that new Arsenal boss Unai Emery is eager to keep Ramsey at The Emirates but the Wales global will be sold if he doesn't agree to a new contract.