The striker will join the Spanish giants on a six-year contract, pending a medical, after the two clubs agreed terms on a transfer on Tuesday morning.
The £62m fee is the largest amount Real have ever paid for a striker. He will also be their third most-expensive signing ever, behind Cristiano Ronaldo and Gareth Bale.
Eintracht Frankfurt’s sporting director Fredi Bobic said: ‘Luka Jovic is a big loss for us. His explosiveness and scoring skills have impressed throughout Europe and we’ve benefited not only from his goals over the past two years.
‘But for us it was clear that there is a financial threshold. For Eintracht Frankfurt this is a good and important transfer. We wish Luka only the best for his future.
‘He has the best qualifications for a great career. And we are proud that we were able to support him along the way.’
Jovic established himself as one of the most in-demand strikers in Europe after a brilliant season for Eintracht.