Torreira has a £21.9 million release clause in his contract, but Arsenal decided to add the extra money to beat Napoli to the the 22-year-olds signature.
The Gunners have offered the midfielder a five-year deal and he will help to add some much-needed solidity in the centre of midfield.
Torreira is Arsenals second signing of the summer after they acquired Juventus defender Stephan Lichtsteiner on a free transfer.
Lichtensteiner is familiar with Torreira after the pair have spent the majority of their careers in Serie A so far, but at other clubs.
They will now link up at The Emirates as Emery attempts to return the north London club back to the top four and beyond.
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Torreira was named in Uruguays provisional 26-man squad for the World Cup this month.
Hes made one appearance for the nation before, and that was in a 2-0 win over the Czech Republic back in March.