The midfielder is currently in Russia as part of the Uruguay squad for the World Cup, and is expected to complete his transfer to the Emirates Stadium once the tournament has finished .
He will become Unai Emery's fourth signing of the summer, having already sealed deals for defender Stephan Lichtsteiner and goalkeeper Bernd Leno . A transfer for centre-back Sokratis Papastathopoulos is due to be confirmed in July as Borussia Dortmund want to wait until their new fiscal year before announcing the move.
New Arsenal boss Emery had targeted a defensive midfielder ahead of the 2018-19 Premier League season, opening talks with the 22-year-old Uruguay international before Jack Wilshere confirmed his departure from the club .
Torreira will join the Gunners after the World Cup, with Sampdoria chief Ferrero announcing the departure on Italian television, highlighting the excellent business the club had done by increasing his price tenfold.
"Sampdoria do not sell unless there are excellent offers," Ferrero told SportItalia .
"We do not look for buyers. We have natural talents whose values increase exponentially.
"Sampdoria is a stepping stone. It's a family-run club and that allows players to grow up. It's normal they have aspirations to play for big clubs, but I do not need to sell out.
"Torreira has left for €30 million. I bought him from Pescara when no one believed.
"We bet and we won, paying just €3 million. The money that comes in is used to keep the club going.
"Sampdoria is a stepping stone. It's a family-run club and that allows players to grow up."