The 22-year-old Uruguay midfielder had a fine World Cup in Russia, matches before the quarter-final defeat to France and on Monday signed a long-term deal with Arsenal.
He has been handed the number 11 shirt for the 2018/19 campaign and will join up with the squad in early August. He eventually made his Serie A debut for Sampdoria in August 2016 and made 71 appearances across two seasons.
Torreira will join on a five-year deal in August after a post-World Cup break.