The two clubs have agreed not to reveal the transfer fee for Jovic, with reports suggesting it is in the region of €60 million (R977 million) plus another €10 million (R163 million) in add-ons.
He said the deal was good for the German club, who originally signed Jovic on a two-year loan from Portuguese club Benfica and took up an option for a permanent move in April after Barcelona showed interest in the Serb who has also scored his first worldwide goal this season.
Jovic scored 27 goals in all competitions this season, helping Frankfurt to the Europa League semi-finals and seventh place in the Bundesliga.
Real Madrid has made quite the splash in the summer transfer window, but it's not for the player you are probably thinking of. "His explosiveness and scoring skills have spread throughout Europe and we've benefited over the past two years, not only from his goals".More news: Serena Williams knocked out of French Open third round by Sofia Kenin
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"But for us it was clear that there is a financial pain threshold".
Jovic is likely to significantly enhance their goal threat next season and Frankfurt sporting director Fredi Bobic admits he will be missed in Germany.
Jovic will be leaving Eintracht Frankfurt after an incredibly successful season and the German club expressed their sadness that the Serbian was leaving the club. "It's an important and good piece of transfer business for Eintracht Frankfurt".
Luka Jovic's signature comes ahead of the much-anticipated move to the Santiago Bernabeu of Chelsea star Eden Hazard, who has always been linked to Real and who indicated after the Europa League final victory over Arsenal that he had played his last game for the Londoners. "We wish Luka only the best for his future", he added. He has all the attributes to have a great career.
The team struggled for goals last season following the departure of Ronaldo to Juventus.