From the letter:

it is clear and logical that United States citizenship alone does not make such individuals immune from being targeted. Rather, it means that the government must take special care and take into account all relevant constitutional considerations, the laws of war, and other law with respect to U.S. citizens....

Such considerations allow for the use of lethal force in a foreign country against a U.S. citizen who is a senior operational leader of al Qaida or its associated forces, and who is actively engaged in planning to kill Americans, in the following circumstances: (1) the U.S. government has determined, after a thorough and careful review, that the individual poses an imminent threat of violent attack against the United States; (2) capture is not feasible; and (3) the operation would be conducted in a manner consistent with applicable law of war principles.

As to targeting al-Awlaki, Holder says:

Al-Aulaqi was a senior operational leader of alQa'ida in the Arabian Peninsula (AQAP), the most dangerous regional affiliate of alQa'ida and a group that has committed numerous terrorist attacks overseas and attempted multiple times to conduct terrorist attacks against the U.S. homeland. And al-Aulaqi was not just a senior leader of AQAP- he was the group's chief of external operations, intimately involved in detailed planning and putting in place plots against U.S. persons. In this role, al-Aulaqi repeatedly made clear his intent to attack U.S. persons and his hope that these attacks would take American lives.

He stresses it was al-Awlaki's actions, not his words, that landed him on the kill list.

But it was not al-Aulaqi's words that led the United States to act against