Well, Obama OLC's legal memo advocated it explicitly, though.

From Wikipedia: 'Barron's memo was described by The New York Times Editorial Board as "a slapdash pastiche of legal theories — some based on obscure interpretations of British and Israeli law — that was clearly tailored to the desired result."[7] A lawyer for the ACLU described the memo as "disturbing" and "ultimately an argument that the president can order targeted killings of Americans without ever having to account to anyone outside the executive branch."[8]'

One could say it "became executive doctrine" then.

What "doctrine" is this? Since World War 1, when the military has deemed it necessary to kill combatants who happen to be American citizens abroad, it has done so.