The 22-year-old delivered convincing performances for the Serie A side last season after teaming up with them on loan.
Aina made 30 league appearances for Walter Mazzarri’s men, scoring once to help Torino finish the season in the seventh spot on the table.
Impressed with the displays from the youngster, the Bull have activated their €10 million option to purchase the wing-back on a permanent basis.
“We’ve redeemed Aina for €10 million, as well as Cristian Ansaldi, and Koffi Djidji. Now Torino own all their players,” Cairo said at the Lega Serie A assembly held in Milan, per Football Italia.
Aina joined Chelsea academy in 2002 and made his senior debut in August 2016 under Antonio Conte.
The defender was limited to three appearances for the Blues and departed the Stamford Bridge Stadium in 2017 to join English Championship side Hull City on loan, where he enjoyed more playing time.
Three-time African champions, Nigeria open their campaign in the biennial tournament against Burundi on June 22, and face Guinea four days later before wrapping up their Group B games against Madagascar on June 30.