The 41-year-old, who first arrived at Ferencvaros as player/coach in September 2008, had been placed in temporary charge of Fradi last month following the dismissal of previous manager Bobby Davison.
Short said: "I'm delighted to take permanent charge of a great club steeped in tradition. We'll now continue planning as we were. I genuinely believe we can get Ferencvaros climbing the table when the seasons starts again after the winter break. We aim to finish in the top five.
"It's by no means an easy challenge. There have been so many problems to overcome in my short spell in charge already, but I'm determined to give it my best shot and see where that takes us."