Hughes: New recruit Granero is the Real deal
Granero, 25, a product of Real's youth set-up who has struggled to establish himself at the Bernabeu, signed a four-year deal at Loftus Road.
"He is a great player, first and foremost," Rangers manager Mark Hughes told the club's website.
"You don't play at a club like Real Madrid if you're not. He is very well regarded there and for him to leave a club of that stature to come to us shows the belief he has in what we are trying to do."
Granero said he was "excited" at the prospect of playing in the Premier League.
"I think QPR will continue to grow as a club and I want to be part of a very bright future here," Granero said.
"I am delighted to be part of this exciting chapter in the club's history. Players that have joined before me are as excited as I am about what QPR can become, one of the great teams in England."
Granero will wear the number 14 shirt at QPR.