The Serb has joined Eintracht Frankfurt on-loan to the end of this season.
Jovic said, "I feel phenomenal and I am more than happy to return to Eintracht, a team that gave me so much. It will be an honor to wear the Eintracht shirt in the coming months.
"Honestly, I have missed many things since I left. I was always aware of the team and the games I was playing while I was away and I am very happy to have been able to return. It is understood that I will do my best to help the team."
Of his 18 months with Real Madrid, he also said: "As a player, I have evolved without any doubt. You have to bear in mind that I have not played regularly for a year and a half and that I will need time to get back to my rhythm.
"I was able to train alongside the best players of the world at Real and I remain optimistic that everything will work out."