1833, from French extradition (18c.), apparently a coinage of Voltaire's, from Latin ex "out" (see ex-) + traditionem (nominative traditio) "a delivering up, handing over," noun of action from tradere "to hand over" (see tradition).
This word might be adopted in our language with advantage, as we have none which conveys the same meaning. Extradition signifies the delivering up of criminals who may have sought refuge in any country, to the government whose subjects they are, on a claim being made to this effect. [from a footnote to the word extradition in the translation of "Memoirs of Marshal Ney" published in London in 1833]