“Agreement has been reached in all areas,” the club said in a statement, adding that the player would be formally unveiled in the coming days.
Financial details have yet to be disclosed.
Isla, 29, joins the club from Italian Serie A side Cagliari. He had a four-year spell at Juventus, punctuated by loans to Queens Park Rangers and Marseille.
Most notably, he has been a regular in the increasingly successful Chile outfit who won the Copa America in 2015 and 2016.
Fenerbahce are looking to reinforce their side after finishing well behind champions Besiktas and surprise runners-up Basaksehir Istanbul in the Turkish Super Lig last season.
Third place meant that Fenerbahce missed out on the Champions League, and only the league title would satisfy their fans next season.
Other signings for Fenerbahce in the close season have included Moroccan international defender Nabil Dirar and French attacking midfielder Mathieu Valbuena.
