The Serbian forward, 21, has been on stunning form this season, netting 17 goals in 31 matches in the Bundesliga.
And according to Sky Germany, Los Blancos have now agreed a five-year contract for the marksman in a deal worth €60m (£52.4m).
He will be Real’s third capture of the transfer window after they managed to secure the services of defender Eder Militao from Porto and Santos forward Rodrygo Goes, who was signed last year.
The news will come as a blow to Chelsea, who have also been strongly linked with Jovic in recent weeks.
Real Madrid boss Zinedine Zidane has been promised a huge overhaul of his current squad, who have had a nightmare campaign this term and sit 18 points behind bitter rivals Barcelona in the LaLiga standings.