The Belgian's number was revealed after the club posted the 2019-20 squad list on their official website.
Hazard signed for Real in June, and his eventual transfer fee could exceed £150 million after he signed a five-year deal to join Los Blancos.
The shirt number was also worn by club legend Emilio Butragueno, who played for Real for a decade and eventually served as director of football and vice-president for the Spanish giants.
Raul was also the No. 7 during his fabled career in the capital.
Expectations are high for Hazard, with Zinedine Zidane overseeing a rebuild of the starting XI at the Santiago Bernabeu Stadium.
Ronaldo's sale severely weakened the attack, and Madrid could only finish third in La Liga last term, 19 points behind champions Barcelona.
Real have struggled in pre-season during Hazard's opening displays. Among other results, the club lost 3-1 to Bayern Munich during the attacker's debut, and they were thrashed 7-3 by neighbours Atletico Madrid in the United States.