The 22-year-old, who is a product of the Blues’ youth system, spent last season on loan with the Serie A club and looks to set to return there permanently.
Speaking to Sky Italy, Torino president Urbano Cairo confirmed that the club have exercised their option to buy Aina with the defender's current deal set to expire at the end of June.
"We exercised our option to buy Ola Aina, as well as [Christian] Ansaldi and [Koffi] Djidji," he said. "Now Torino own all their players."
Aina plays predominately as a right-back, but is capable of playing as a wing-back or wide midfielder.
He previously spent the 2017/18 campaign on loan at Championship outfit Hull City, where he made 44 league appearances.
At Torino, Aina was equally as important and he played 30 of the Turin-based outfit’s 38 Serie A matches last year.
The defender has made six appearances for the Chelsea first team, three of which came in the cup competitions and three in the Premier League.
Aina is also a Nigeria international and has earned eight caps for the national side, the last of which came in October.
Given Chelsea’s impending transfer embargo, in which the club are restricted from signing players for the next two windows, added importance has been given to the club’s numerous returning loan players, several of whom could force their way into the first-team picture at Stamford Bridge in 2019/20.
Chelsea currently only have Cesar Azpilicueta and David Zappacosta as the club’s recognised right-backs, and Reece James could therefore be expected to compete with the duo for a starting berth.
Among the numerous loan signings expected to play a part next year for the Blues are: Tammy Abraham, who helped fire Aston Villa back to the Premier League, French defender Kurt Zouma, who was at Everton and Mason Mount, who spent the previous campaign under the tutelage of former Chelsea legend Frank Lampard.
While the London club look unlikely to welcome any new signings to the Bridge this summer, they can look forward to the arrival of Christian Pulisic. The American was signed by Chelsea in January but immediately loaned to former club Dortmund.