The Serbia international, 21, joined from Eintracht Frankfurt for a reported 60m euros last week.
Jovic scored his second goal in his sixth appearance for Serbia as they beat Lithuania 4-1 in Euro 2020 qualifying on Monday.
Last season he scored 27 goals in 48 games for the German club.
He was also named in Uefa’s Europa League squad of the season after scoring 10 goals on their run to the semi-finals, where they lost on penalties to eventual winners Chelsea.
“Now I’m the happiest kid in the world having signed a contract with the biggest club,” he said. “I’m going to give everything to help Real Madrid win more trophies and titles.”
The former Red Star Belgrade and Benfica player has won league titles in Portugal and Serbia and the German Cup with Frankfurt.
“Our fans are going to ask you for a lot more because they know everything you can offer with your great quality,” said Real president Florentino Perez. “So you have before you the greatest challenge of your career”.
Jovic was signed days before Real announced they had agreed a deal for Chelsea forward Eden Hazard for a fee that could exceed £150m.
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