Sanchez spent seven years at the Santiago Bernabeu from 1985 to 1992 and was La Liga's top-scoring foreign player until he was surpassed by Barcelona's Lionel Messi earlier this year.
But Hernandez, who joined on loan from Manchester United on Monday, insists he will not try to model himself on his compatriot during his time at the club.
"Playing for Real Madrid is a dream come true," said the striker. "Around the world people know all about this team.
"Hugo Sanchez made a great career here, but I come to do my own thing, and that is to give everything to help the team.
"I'm a person who is totally dedicated. A professional player on and off the field.
"I will give 100 per cent to respond to the confidence they have shown in me and help them get the titles, which is the requirement for this club.
"I see the challenge of Real Madrid with great joy and motivation. Not all players can wear this shirt. "
Hernandez could feature when Real host local rivals and Spanish champions Atletico after the international break.
