The 29-year-old will join a select list of Ghanaian footballers to have worked with the former Inter Milan manager, including Michael Essien and Sulley Muntari.
The Turkish giants unveiled Mourinho as their new head coach on Sunday, with thousands of fans showing up at the Sukru Saracoglu Stadium to welcome him.
A two-time UEFA Champions League winner, Mourinho’s last job was at AS Roma, where he led the Italian club to win the UEFA Europa Conference League.
As Fenerbahce manager, the former Chelsea and Real Madrid boss will be aiming to return the club to the pinnacle of Turkish football after they lost the league title to rivals Galatasaray in the just-ended season.
"I want to thank you for your love, the love that I felt from the first moment where my name was first connected with Fenerbahce," Mourinho said at his unveiling, as quoted by Sky Sports.
"Normally, a coach is loved after victories. In this case, I feel that I am loved before victories. That, for me, is a big responsibility that I feel. I promise you that from this moment I belong to your family. This shirt is my skin.
"Football is passion and there is no better place to feel that passion. Since the moment I met with President Ali Koc I wanted to play for you because in the end, you are the soul of the football club.”
Meanwhile, Djiku has been a key player at Fenerbahce since joining the club in the summer of 2023 on a free transfer after parting ways with Ligue 1 side Racing Strasbourg.
He made 36 appearances in all competitions for Fenerbahce last season, contributing three goals and two assists.
The centre-back is currently with the Ghana national team as they prepare to face Mali and the Central African Republic (CAR) in the 2026 FIFA World Cup qualifiers.