The 22-year-old former Birmingham City midfielder has put pen to paper on a three-and-a-half-year deal.
Kilkenny arrived at Elland Road as an emergency loan signing in time to make an impressive debut in the 3-0 home win over Northampton.
The Australia international had only just completed a second loan spell at Oldham and was in the Latics side that beat Leeds 3-1 at Elland Road on New Year's Day.
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