The 25-year-old Netherlands international completed his move to the Spanish champions from Ajax aftersigning a contract until 2013, and was given the number 19 shirt.
He moved for a fee of 20 million euros ($25.24 million) with a further seven million payable on variables, and will replace the injured Van Nistelrooy at the head of Real's attack.
The former Manchester United forward has been ruled out for the rest of the season with a knee injury, and is one of a number of players on Real's extensive absentee list.
"Van Nistelrooy is a fantastic player but I am a different type of player, and will do what I can to score as many goals as possible," Huntelaar told a news conference.
"Everything has happened very quickly. I was going to come at the end of the season but because of the injuries it was brought forward."
The Dutchman will not be eligible to turn out for Real until the January transfer window opens when his first game could be against second-placed Villarreal at the Bernabeu.
But first he has to recover from an ankle ligament injury that has kept him sidelined since last month.
"It's still a little sore. Although it is not perfect, I hope to return to action soon," Huntelaar added.
(Writing by Mark Elkington; editing by Miles Evans)
