"The Montana regional court has decided in favour of the extradition of Tsvetan Tsvetanov to Austria," Svetla Stanimirova, spokeswoman for the court in northwestwern Bulgaria, told AFP.
The 32-year-old man, arrested in Bulgaria shortly after the tragedy, is charged with the negligent manslaughter of the 71 people plus belonging to a criminal gang.
He allegedly drove the refrigerated truck, the discovery of which on August 27 prompted revulsion throughout Europe, at least some of its journey from Hungary into Austria.
"My client is innocent. It was us who requested the extradition to Austria because there is no other way to prove his innocence," his lawyer Svetlin Slavkov said Tuesday.
"He is even ready to give a DNA sample."
The 59 men, eight women and four children are believed to have suffocated up to two days before the lorry's discovery on the side of the A4 motorway near Vienna.
Last week police said that only 10 of the victims have been identified so far, all of them Iraqis.
Another five men, four Bulgarians and an Afghan, have so far been detained in Hungary over the case, which highlighted the role of trafficking gangs transporting migrants into Europe.