1630s, "authoritative sanction," from Latin fiat "let it be done" (used in the opening of Medieval Latin proclamations and commands), third person singular present subjunctive of fieri "be done, become, come into existence" (from PIE root *bheue- "to be, exist, grow"), used as passive of facere "to make, do." Meaning "a decree, command, order" is from 1750. In English the word also sometimes is a reference to fiat lux "let there be light" in Genesis i.3.
Dixitque Deus: Fiat lux. Et facta est lux. [Vulgate]