The team said a six-year contract for the 21-year-old is pending a physical.
Luka Jovic joins Real Madrid: Five key things to know...
Jovic joined Frankfurt on loan from Benfica in 2017 and in April the Bundesliga club exercised their option to make the move permanent.
Jovic has shown his ambipedal nature, scoring 15 right-footed goals and eight with his left foot - in addition to four headers.
Jovic will earn him £43.7m (€50m) in total or £8.7m a year.
Jovic originally belonged to Benfica, but after a season in Germany, Eintracht took over their rights and has now made a decision to sell their star player to Real Madrid.
While both clubs have chose to keep the fee secret, it is widely reported to be in excess of £50m.
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According to AS, Fredi Bobic, Eintracht's sporting director said, "On a sporting front, Luka Jovic leaving is a big loss for us". "His explosiveness and capacity to score goals propelled us into Europe and we have benefited from more than just his goals in the past two years".
"But it was clear to us that there was a financial pain threshold".
"It's an important piece of transfer business for Eintracht Frankfurt, and a good one as well". We wish Luka all the best in the future.
"He has the best perspectives for a brilliant career. We are proud to have helped him on his way", he said.
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Real were expected to spend big this summer after enduring a testing 2018-19 campaign. After nine goals in his first season, he managed to find the back of the net 27 times in his second season.
A masterful movement by Real Madrid, who are looking to strengthen their squad after a disappointing season.