The 34-year-old has agreed a three-year contract to link up with former Rangers manager Neil Warnock at Elland Road.
Kenny was named Rangers' player of the year as they secured promotion back to the Barclays Premier League in 2010/11, and missed just five matches last season.
But QPR's capture of England keeper Robert Green from West Ham last month has paved the way for Kenny to move back to Yorkshire, having also played under Warnock at Sheffield United.
"We've worked very hard with this one," Warnock told the club's official website. "It's taken some time to get over the line, but I think he's the most important signing I'll make while I'm at Leeds United. I rate him that highly and I think the fans will see why.
"I didn't think we'd be able to get him. There's no way I would have let him go. I wouldn't have swapped him for anybody they have on their books. I think he's a great keeper. He's one of the best in the country, not just the Championship. We're delighted to get him.
Kenny added when speaking to QPR's official website: "I've loved every single minute of my time at QPR.
"It's been an incredible two years. Winning promotion to the Premier League here is an experience I will never forget as was the rollercoaster ride of avoiding relegation last season. Hopefully I'll be back at Loftus Road as a Premier League player with Leeds United in the very near future."