The move reunites the Republic of Ireland international with QPR manager Neil Warnock, who signed him for the Blades from Bury in 2002.
Warnock told QPR's official website: "Paddy has made mistakes in his life but he's a straightforward guy and I think this is the right time for him to leave Sheffield and focus on the next chapter of his career.
"I rate him very, very highly."
Kenny added: "The chance to work with Neil again was too good an opportunity to turn down."
Kenny played 278 times for United in his eight years at Bramall Lane.
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