Where exactly is this authority granted under the Constitution?
Article II, Section 2 of the Constitution states:
The President shall be commander in chief of the Army and Navy of the United States, and of the militia of the several states, when called into the actual service of the United States....
Article I, Section 8 of the constitution states that Congress shall have the power to:
..declare war, grant letters of marque and reprisal, and make rules concerning captures on land and water;
To raise and support armies, but no appropriation of money to that use shall be for a longer term than two years;
To provide and maintain a navy;
and To make rules for the government and regulation of the land and naval forces
However, the War Powers Act of 1973, (the purpose of which is stated to be: "...to fulfill the intent of the framers of the Constitution of the United States and insure that the collective judgement of both the Congress and the President will apply to the introduction of United States Armed Forces into hostilities, or into situations where imminent involvement in hostilities is clearly indicate by the circumstances, and to the continued use of such forces in hostilities or in such situations."), clearly states in Section III that:
"The President in every possible instance shall consult with Congress before introducing United States Armed Forces into hostilities or into situation where imminent involvement in hostilities is clearly indicated by the circumstances, and after every such introduction shall consult regularly with the Congress until United States Armed Forces are no longer engaged in hostilities or have been removed from such situations."
No where is the authority granted specifically to the President to, (as you say), "deploy troops anywhere outside the United States he desires for any reason." Nor does he "have complete authority over US armed forces in both wartime and peacetime."
If I remember correctly the War Powers Act was Congress’ response to avoid another “Viet Nam” scenario. It was supposed to limit the power of any President who deployed troops in an open-ended engagement without a declaration of war by Congress. Nixon vetoed the bill but Congress overrode it. No one to my knowledge has ever brought up the constitutionality of the War Powers Act before the Supreme Court.
Of course it is.
He is specifically and explicitly made Commander In Chief of America's military forces.
Not "Commander In Part" or "Commander To A Certain Extent."
The law requires him to update Congress on his decisions and discuss his decisions with them (which he should obviously be doing anyway) and requires him to rely on Congress to fund the military budget, but as Commander In Chief he has full discretion to send our military forces anywhere in the world for any purpose that national security requires according to his lights.
Unless the word "Commander" has some secret meaning known only to Paulestinians to which lesser beings are not privy.