Letter to Brigadier-General Nelson, 20 August 1778, in Ford's Writings of George Washington (1890), vol. VII, p. 161. Part of this is often attached to a fragment of a letter to John Armstrong of 11 March 1782; it is also often prefaced with the spurious "governing without God" sentence, as this 1867 example from Henry Wilson (Testimonies of American Statesmen and Jurists to the Truths of Christianity) shows:
It is impossible to govern the world without God. It is the duty of all nations to acknowledge the Providence of Almighty God, to obey his will, to be grateful for his benefits and humbly implore his protection and favor. I am sure there never was a people who had more reason to acknowledge a divine interposition in their affairs, than those of the United States; and I should be pained to believe that they have forgotten that agency which was so often manifested during the revolution; or that they failed to consider the omnipotence of Him, who is alone able to protect them. He must be worse than an infidel that lacks faith, and more than wicked, that has not gratitude enough to acknowledge his obligations.
1770s
Context: It is not a little pleasing, nor less wonderful to contemplate, that after two years' manoeuvring and undergoing the strangest vicissitudes, that perhaps ever attended any one contest since the creation, both armies are brought back to the very point they set out from, and that which was the offending party in the beginning is now reduced to the use of the spade and pickaxe for defence. The hand of Providence has been so conspicuous in all this, that he must be worse than an infidel that lacks faith, and more than wicked, that has not gratitude enough to acknowledge his obligations. But it will be time enough for me to turn preacher, when my present appointment ceases…