Objection 1. It would seem that intention is an act of the intellect, and not of the will. For it is written (Matthew 6:22): "If thy eye be single, thy whole body shall be lightsome": where, according to Augustine (De Serm. Dom. in Monte ii, 13) the eye signifies intention. But since the eye is the organ of sight, it signifies the apprehensive power. Therefore intention is not an act of the appetitive but of the apprehensive power.
Objection 2. Further, Augustine says (De Serm. Dom. in Monte ii, 13) that Our Lord spoke of intention as a light, when He said (Matthew 6:23): "If the light that is in thee be darkness," etc. But light pertains to knowledge. Therefore intention does too.
Objection 3. Further, intention implies a kind of ordaining to an end. But to ordain is an act of reason. Therefore intention belongs not to the will but to the reason.
Objection 4. Further, an act of the will is either of the end or of the means. But the act of the will in respect of the end is called volition, or enjoyment; with regard to the means, it is choice, from which intention is distinct. Therefore it is not an act of the will.
On the contrary, Augustine says (De Trin. xi, 4,8,9) that "the intention of the will unites the sight to the object seen; and the images retained in the memory, to the penetrating gaze of the soul's inner thought." Therefore intention is an act of the will.
I answer that, Intention, as the very word denotes, signifies, "to tend to something." Now both the action of the mover and the movement of thing moved, tend to something. But that the movement of the thing moved tends to anything, is due to the action of the mover. Consequently intention belongs first and principally to that which moves to the end: hence we say that an architect or anyone who is in authority, by his command moves others to that which he intends. Now the will moves all the other powers of the soul to the end, as shown above (Question 9, Article 1). Wherefore it is evident that intention, properly speaking, is an act of the will.
Reply to Objection 1. The eye designates intention figuratively, not because intention has reference to knowledge, but because it presupposes knowledge, which proposes to the will the end to which the latter moves; thus we foresee with the eye whither we should tend with our bodies.
Reply to Objection 2. Intention is called a light because it is manifest to him who intends. Wherefore works are called darkness because a man knows what he intends, but knows not what the result may be, as Augustine expounds (De Serm. Dom. in Monte ii, 13).
Reply to Objection 3. The will does not ordain, but tends to something according to the order of reason. Consequently this word "intention" indicates an act of the will, presupposing the act whereby the reason orders something to the end.
Reply to Objection 4. Intention is an act of the will in regard to the end. Now the will stands in a threefold relation to the end. First, absolutely; and thus we have "volition," whereby we will absolutely to have health, and so forth. Secondly, it considers the end, as its place of rest; and thus "enjoyment" regards the end. Thirdly, it considers the end as the term towards which something is ordained; and thus "intention" regards the end. For when we speak of intending to have health, we mean not only that we have it, but that we will have it by means of something else.
Source: Summa Theologica (New Advent)