Fer played 29 times for Norwich last season and also starred at the World Cup with the Netherlands over the summer.
He becomes Harry Redknapp's fifth signing of the transfer window, joining Rio Ferdinand, Steven Caulker, Mauricio Isla and Jordon Mutch in west London.
"I can't wait to get started here," he said. "It was always my dream to stay in England, in the Premier League. QPR did well last season to come up and the squad is full of top players, so I'm delighted to be here.
"Harry told me I was a big target for him and when you hear that from a coach, you want to work with them and play for them. I'm just looking forward to showing what I'm capable of here at QPR."
Redknapp said: “He will be an excellent signing – a Dutch international who played in the World Cup. He is an outstanding midfield player and will bring a lot of qualities to the club. It is a massive boost and I'm delighted we've been able to get him to QPR.
"He's got a great physique, gets box to box - I think he'll be a good signing for us. We were a bit light (in midfield). You need cover everywhere."
Sky sources understand that although the fee is £7million it could be worth as much as £10million to Norwich in add-ons and player giving up loyalty payments.