The veteran defender, who left Aston Villa this summer at the end of his contract, becomes the Championship club's second signing of the summer.
Rs manager Harry Redknapp hailed the 33-year-old's signing and moved to allay fears over his fitness record after he failed to make a single appearance for Villa last term due to a hip complaint.
"This is a great signing for us. He's a top-class defender and a great guy. He's a good character and just what we need," Redknapp told the club's official website.
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"Obviously he had his problems last season with the injury but 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, who began his career in England with Everton before stints at Manchester City and Villa, expressed his excitement over the prospect of working with Redknapp.
"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," he enthused.
"I know the club didn't have a good season last term but – having spoken to Harry, as well as Tony [Fernandes, chairman] – 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."