The Republic of Ireland defender left Aston Villa earlier this summer and arrives at Loftus Road on a free transfer.
Dunne has signed a one-year contract and joins fellow Bosman signing Danny Simpson at QPR ahead of the Championship season.
The 33-year-old missed the whole of last season with an Achilles injury but was fit enough to appear as a substitute for Ireland against Georgia last month.
And Rangers will not be left out of pocket if the injury recurs during the forthcoming campaign.
Harry Redknapp told the club website: "There's an agreement in place that if he breaks down, the contract can be ended.
"He's confident he'll be okay and, from our point of view, if he doesn't have any problems with it then we've just signed a very, very good centre-half."
Dunne said: "I've been very close to signing for Harry on a couple of occasions and the opportunity to work with him really appealed to me. Players want to play for Harry and I'm no different.
"I know the club didn't have a good season last term but, having spoken to Harry as well as chairman Tony Fernandes, there's a real determination to bounce back into the Premier League, which is where we all want to be.
"I've played in the Championship and won it with Manchester City, so hopefully my experience will benefit the team over the course of the season. It's a good challenge for me and one I'm very excited about."