[fee-aht, -at; fahy-uht, -at]
an authoritative decree, sanction, or order: a royal fiat. authorization, directive, ruling, mandate, diktat, ukase.
a fixed form of words containing the word fiat, by which a person in authority gives sanction, or authorization.
an arbitrary decree or pronouncement, especially by a person or group of persons having absolute authority to enforce it: The king ruled by fiat.

1625–35; < Latin: let it be done, 3rd singular present subjunctive of fierī to become Unabridged

fiat justitia, ruat caelum

[fee-aht yoos-tee-tee-ah roo-aht kahy-loom; English fee-aht juhs-tish-ee-uh roo-at see-luhm, fahy-uht]
let there be justice though the heavens fall.

fiat lux

[fee-aht looks; English fee-aht luhks, fahy-uht]
let there be light. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
fiat (ˈfaɪət, -æt)
1.  official sanction; authoritative permission
2.  an arbitrary order or decree
3.  literary chiefly any command, decision, or act of will that brings something about
[C17: from Latin, literally: let it be done, from fierī to become]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

late 14c., from fiat lux "let there be light" in the Book of Genesis, from L. fiat "let it be done" (also used in the opening of M.L. proclamations and commands), third person singular present subjunctive of fieri, used as passive of facere "to make, do" (see factitious).
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Abbreviations & Acronyms
Italian Fabbrica Italiana Automobili Torino (Italian Automobile Factory of Turin)
The American Heritage® Abbreviations Dictionary, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Example sentences
Industries that depend on government fiat for their livelihood are living on
  borrowed time.
If only our hominid ancestor's descendants could learn to use fiat currency,
  think of the evolution that might yet await.
Every major economy in the world now uses fiat currency which are bits of
  colored paper.
Fiat has gone so far as to give drivers extremely detailed report cards of how
  to improve their fuel economy.
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