It started under Washington, albeit there were phases of lesser action, with another phase coming into effect during Jefferson's term.
He said that he had done all he could without a Declaration of War from Congress. His successor, Alexander Hamilton, disagreed. Hamilton said that the Pirates had already declared war on the United States, so he wasn't required to wait for a Declaration of War.
His Successor? Hamilton Was President?
Their disagreement was on how broad that authority was. BOTH agreed that the President could carry out war if the nation was attacked, without a Congressional Declaration of War. Congress specifically allocated funds for that action, and for the one we are currently engaged in.
Declaration of War
In the early draft of the Constitution presented to the Convention by its Committee of Detail, Congress was empowered ''to make war.''1412 Although there were solitary suggestions that the power should better be vested in the President alone,1413 in the Senate alone,1414 or in the President and the Senate,1415 the sentiment of the Convention, as best we can determine from the limited notes of the proceedings, was that the potentially momentous consequences of initiating armed hostilities should be called up only by the concurrence of the President and both Houses of Congress.1416 In contrast to the English system, the Framers did not want the wealth and blood of the Nation committed by the decision of a single individual;1417 in contrast to the Articles of Confederation, they did not wish to forego entirely the advantages of executive efficiency nor to entrust the matter solely to a branch so close to popular passions.1418
The result of these conflicting considerations was that the Convention amended the clause so as to give Congress the power to ''declare war.''1419 Although this change could be read to give Congress the mere formal function of recognizing a state of hostilities, in the context of the Convention proceedings it appears more likely the change was intended to insure that the President was empowered to repel sudden attacks1420 without awaiting congressional action and to make clear that the conduct of war was vested exclusively in the President.1421