The Gunners completed a deal to sign the Uruguay international in a big money deal from Serie A side Sampdoria following weeks of speculation.
Torreira, who commanded a reported £26m transfer fee, has put pen to paper on a long-term deal with the north London side.
The Uruguayan will be tasked with improving Unai Emery’s options in the middle of the park following Jack Wilshere’s exit this summer.
Torreira impressed during the World Cup with a series of combative performances, including an excellent display in Uruguay’s 2-1 win over Cristiano Ronaldo and his Portugal team.
Arsenal supporters were eagerly awaiting news of Torreira’s proposed move to the Emirates Stadium during the World Cup after watching his eye-catching performances in Russia.
The new Arsenal signing sent a message of thanks to the Gunners supporters after the holding midfielder completed a move on Tuesday evening.
“Yes, for a while I’ve been receiving loads of messages in my social media accounts,” Torreira told Arsenal’s website.
“I guess it’s all down to the fact there were talks of me moving to Arsenal even before the World Cup started. I am very happy and I hope I can meet all the fans very soon.”
Arsenal haven’t won the Premier League title since 2003-04.
In fact, the Gunners have failed to finish in the Premier League’s top four in Arsene Wenger’s final two seasons in charge.
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