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.
On the up: Short (top) is now in the hotseat at the Hungarian club
'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.'
Former Notts County, Derby, Everton and Blackburn centre-half Short, who spent the final two years of his playing career with the Blades, retired from football in 2006 to focus on his sailing business on Lake Windermere.
He played a key role in Blackburn's promotion back to the Premier League in 2001 and helped the Blades in their successful climb back to the top flight in 2006.
A spokesman for Ferencvaros said: 'Craig Short will continue to be head coach of Ferencvaros.
'The board will be announcing a new football and commercial strategy on December 21. This will add to the management team of Ferencvaros both on and off the pitch.'
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