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.
LATEST FOOTBALL NEWS
How Chelsea could line-up in Europa League final without Loftus-Cheek
Warburton on financial restraints and who he blames for his Twitter account
Southgate confirms Loftus-Cheek injury with Chelsea midfielder ‘facing year out’
Reports earlier this week claimed an agreement has already been reached between the Bernabeu club and the Blues over Hazard’s transfer, with an £87million (€100m) fee to be paid for his services.
The deal is said to have been reached ‘several weeks ago’, with Real’s announcement of Hazard’s capture to be made after the Europa League final at the end of the month.
Football Index Futures
Become a Football Futures Trader on
Trade £500 RISK FREE for 7 Days.
- Build your Portfolio
- Earn Dividends
- Sell at a Profit!
Get started from just £10 Learn more - join.fifutures.com