Varga has impressed at Burnley
The towering centre-half spent January on-loan at Turf Moor, and participated in Burnley's battling display against Arsenal. He was expected to return to Sunderland at the end of this month but has impressed Owen Coyle and his staff.
The 35-year-old Slovakian's Sunderland contract ends this summer and it remains to be seen whether he will feature for the Black Cats again after making no appearances this season.
There is no recall clause in the deal.