Burnley boss Owen Coyle said: "I have known him for years, both from when I played against him and during my time as a coach and manager.
"In the light of our injuries and suspensions, he will bring a physical presence to the backline."
Varga has been allowed to leave the Stadium of Light as he is not in manager Roy Keane's plans.
Coyle added: "I'm delighted to get Varga on loan. I'm sure he will compliment the squad and have a big impact on the team."