The 32-year-old has reportedly passed a medical at Loftus Road and has agreed personal terms on a £750,000 move.
Kenny is set to be reunited with former Blades boss Neil Warnock, and it will be the third time the experienced manager has signed the shot-stopper.
Kenny sat out a large amount of last season after testing positive for banned substance ephedrine and was suspended for nine months back in September.
But he returned at the end of the campaign and is now set for a switch to the London club.
Warnock said: “It’s the third time I’ve signed Paddy and I’m delighted to be linking up with him again. There were times when it was him or Shay Given for the Irish spot, and in my opinion Paddy didn’t get the recognition he deserved.
“It’s well known he’s made mistakes in the past but he’ll be a great capture for QPR and I’m sure he’s going to be popular in the changing room and with our fans.”