It's not an easy question.  The President and his agents certainly have the authority to kill Americans actively engaged in treason.  That authority is strongest on the battlefield.  The further you are from the battlefield, the more tenuous the authority becomes.  

Yemen was not a U.S. war zone.  Yemen at the time was a country in which the U.S. was aiding a repressive regime involved in a complex civil war with international connections.  The manner in which the Constitution defines treason and how it shall be established argues against a power of summary execution for treason by the President:

 Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort. No Person shall be convicted of Treason unless on the Testimony of two Witnesses to the same overt Act, or on Confession in open Court.

The Congress shall have Power to declare the Punishment of Treason, but no Attainder of Treason shall work Corruption of Blood, or Forfeiture except during the Life of the Person attainted.


That's Article III Sec. 3.  Article III is the part of the Constitution that establishes the judicial power of the United States.  There is no mention of the President in its passages, and the language of "Testimony of two Witnesses...or on Confession in open Court" does not lend itself to supporting assassination at the order of the President.  Had John Walker Lindh been killed in action by U.S. forces or our allies instead of being captured in an al Qaeda camp, I don't think anyone would have argued that was an unlawful deprivation of due process.  It would not have been an ordered assassination, either.  Al Awlaki was not killed in battle with a weapon in his hand, surrounded by and supporting the foes of the United States.  

“Nobody has a legitimate reason to fear a faithful interpretation of the Constitution, and nobody has any legitimate reason to fear effective and complete protection of civil rights." - Alan Gura