The Gunners did offer the player to undergo a medical in Russian Federation, but the player rejected as he wanted to commit wholly on national duty.
The transfer - rumoured to be in the £26 million region - was in advanced stages last month but hit delays when Torreira joined up with the Uruguayan squad for this summer's World Cup in Russian Federation.
Torreira has a £22.1m (€25m) release clause in his Sampdoria contract but Arsenal have made a decision to pay a premium so they can spread out the payments.
Although the Uruguay midfielder hasn't officially completed his move yet, all the indications suggest an announcement will come mere days after he returns from Russian Federation.
But he also said that the deal is on and the 22 year old will eventually be joining Arsenal as soon as the campaign ends for Uruguay.
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At this point, though, it's only a matter of time before the deal is completed, with Torreira set to join fellow new signings Sokratis and Stephan Lichtsteiner at the Emirates.
The Sampdoria midfielder's involvement at the World Cup ended on Friday as Uruguay crashed out at the quarter final stage following a 2-0 defeat against France.
"I bought him from Pescara when no one believed".
It's fair to say Arsenal fans will be happy if Torreira proves to be half the player Kante has been in England. "We placed a bet and we won, paying just €3m".
Those players not on World Cup duty have already returned for the start of pre-season training, with a first warm-up fixture set against Boreham Wood at Meadow Park on Saturday.