The 21-year-old Serbia worldwide emerged as one of the most sought-after talents in European football during the 2018-19 campaign.
Jovic will earn him £43.7m (€50m) in total or £8.7m a year.
Frankfurt had loaned Jovic from Benfica for the past two seasons and due to a permanent signing clause in his contract were able to purchase the Serbian worldwide for a fee believed to be around €7 million (£5.96m).
Jovic, considered one of the hottest young prospects in European football, scored 27 goals in all competitions in 2018/19, helping Frankfurt to the Europa League semi-finals and a seventh-place finish in the Bundesliga.
After coming through at Red Star, where he made his first-team debut in 2013-14, he moved to Benfica, where he played for the B team and the first team.
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While both clubs have chose to keep the fee secret, it is widely reported to be in excess of £50m.
Luka Jovic had always been seen as a highly promising striker in his homeland, Serbia. "His explosiveness and goal threat are now known around Europe".
"But for us it was clear that there is a financial pain threshold". He has the best conditions for a great career. For Eintracht Frankfurt this is a good and important transfer.
"From a sporting point of view, Luka Jovic is a huge loss for us", Frankfurt chairman Fredi Bobic said. "And we are proud that we have supported him on his way".
Jovic will compete with French forward Karim Benzema at Madrid, which also has forwards Gareth Bale, Lucas Vazquez, Mariano Diaz and Vinicius Junior.
Jovic is Zinedine Zidane's third signing of the summer, with a big rebuilding project underway after a disastrous 2018-19 campaign.