When and how was the doctrine of the one divine will established? Many (perhaps most) Trinitarian theologians says that the Father, Son, and Spirit each possess the one singular divine will. This is a stronger statement than saying they are "united in will", which could leave open the possibility that each person of the Trinity has its own will. (In the incarnation the Son took on a human nature including a human will, but that is out of scope for this question. Answers should not focus on the incarnation or Christology. This question is about the one divine will possessed by the Father, Son, and Spirit in eternity.)

When was this doctrine first expounded, and what arguments, whether Biblical or otherwise, were given to support it?

Another question, Does the triune God have will by nature, or by persons?, has some good information and quotes about this doctrine, but it does not ask about the earliest defences of it.
Gregory of Nazianzus (329-390) in his Fourth Theological Oration gives an early defence for the doctrine of the one divine will. The context of this paragraph is John 6:38.


  Let them quote in the seventh place that The Son came down from Heaven, not to do His own Will, but the Will of Him That sent Him.  Well, if this had not been said by Himself Who came down, we should say that the phrase was modelled as issuing from the Human Nature, not from Him who is conceived of in His character as the Saviour, for His Human Will cannot be opposed to God, seeing it is altogether taken into God; but conceived of simply as in our nature, inasmuch as the human will does not completely follow the Divine, but for the most part struggles against and resists it.  For we understand in the same way the words, Father, if it be possible, let this cup pass from Me; Nevertheless let not what I will but Thy Will prevail.  For it is not likely that He did not know whether it was possible or not, or that He would oppose will to will.  But since, as this is the language of Him Who assumed our Nature (for He it was Who came down), and not of the Nature which He assumed, we must meet the objection in this way, that the passage does not mean that the Son has a special will of His own, besides that of the Father, but that He has not; so that the meaning would be, “not to do Mine own Will, for there is none of Mine apart from, but that which is common to, Me and Thee; for as We have one Godhead, so We have one Will.”  For many such expressions are used in relation to this Community, and are expressed not positively but negatively; as, e.g., God giveth not the Spirit by measure, for as a matter of fact He does not give the Spirit to the Son, nor does He measure It, for God is not measured by God; or again, Not my transgression nor my sin.  The words are not used because He has these things, but because He has them not.  And again, Not for our righteousness which we have done, for we have not done any.  And this meaning is evident also in the clauses which follow.  For what, says He, is the Will of My Father?  That everyone that believeth on the Son should be saved, and obtain the final Resurrection.  Now is this the Will of the Father, but not of the Son?  Or does He preach the Gospel, and receive men’s faith against His will?  Who could believe that?  Moreover, that passage, too, which says that the Word which is heard is not the Son’s but the Father’s has the same force.  For I cannot see how that which is common to two can be said to belong to one alone, however much I consider it, and I do not think any one else can.  If then you hold this opinion concerning the Will, you will be right and reverent in your opinion, as I think, and as every right-minded person thinks.