The 23-year-old midfielder had already agreed personal terms with Madrid on Wednesday and will sign a five-year deal with the Merengues after undergoing a medical.
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Date of Birth: 4 April 1987
Place of Birth: Stuttgart, Germany
Height: 189 cm
Position: Holding midfielder
"Sami Khedira is a true leader on the pitch and he personifies everything that Stuttgart stand for. Therefore, it's not easy to let go of him," said Stuttgart sporting director Fredi Bobic on the official Stuttgart website.
"However, on the other hand, we couldn't deny Sami his dream move to Real Madrid. We'd like to wish him all the best at his new club."
Khedira had attracted the interest of Real Madrid with his excellent performances for Germany at the 2010 World Cup and was since continually being linked with a move to the Spanish powerhouse.
The midfielder is a product of the Stuttgart youth academy and has made over 100 official appearances for the Schwaben since making his debut in October 2006.