The 25-year-old midfielder was a product of Real's youth system but played only sporadically for the first team, convincing him it was time to leave.
"It wasn't a hard decision to come here. I'm hungry and here I will be able to grow as a player," the Spaniard said.
"Real Madrid is a great club, I have played there since I was eight. I spent three years in the first team and I will always be thankful to them.
"But it was time to change and the best way to do that was join QPR.
"Since two weeks ago my thoughts are here and I don't miss anything about Real.
"Everyone at the club trusts me and that's all I needed. I know I've made the right decision."
Big-spending Rangers have started the season slowly but Granero believes they will soon start climbing the table.
"There are a lot of new players here so we must get to know each other first," he said.
"We must improve, but this team will do that when it spends more time together.
"One point from the first three games is not unexpected, but this is not the way it will remain.
"This season will be great - I can see that in my team-mates' faces. There are quality players here, so just give us time."