Objection 1. It would seem that consent is not the efficient cause of matrimony. For the sacraments depend not on the human will but on the Divine institution, as shown above (Sent. iv, D, 2; III, 64, 2). But consent belongs to the human will. Therefore it is no more the cause of matrimony than of the other sacraments.
Objection 2. Further, nothing is its own cause. But seemingly matrimony is nothing else than the consent, since it is the consent which signifies the union of Christ with the Church.
Objection 3. Further, of one thing there should be one cause. Now there is one marriage between two persons, as stated above (Question 44, Article 1); whereas the consents of the two parties are distinct, for they are given by different persons and to different things, since on the one hand there is consent to take a husband, and on the other hand consent to take a wife. Therefore mutual consent is not the cause of matrimony.
On the contrary, Chrysostom [Hom. xxxii in the Opus Imperfectum, falsely ascribed to St. John Chrysostom] says: "It is not coition but consent that makes a marriage."
Further, one person does not receive power over that which is at the free disposal of another, without the latter's consent. Now by marriage each of the married parties receives power over the other's body (1 Corinthians 7:4), whereas hitherto each had free power over his own body. Therefore consent makes a marriage.
I answer that, In every sacrament there is a spiritual operation by means of a material operation which signifies it; thus in Baptism the inward spiritual cleansing is effected by a bodily cleansing. Wherefore, since in matrimony there is a kind of spiritual joining together, in so far as matrimony is a sacrament, and a certain material joining together, in so far as it is directed to an office of nature and of civil life, it follows that the spiritual joining is the effect of the Divine power by means of the material joining. Therefore seeing that the joinings of material contracts are effected by mutual consent, it follows that the joining together of marriage is effected in the same way.
Reply to Objection 1. The first cause of the sacraments is the Divine power which works in them the welfare of the soul; but the second or instrumental causes are material operations deriving their efficacy from the Divine institution, and thus consent is the cause in matrimony.
Reply to Objection 2. Matrimony is not the consent itself, but the union of persons directed to one purpose, as stated above (Question 44, Article 1), and this union is the effect of the consent. Moreover, the consent, properly speaking, signifies not the union of Christ with the Church, but His will whereby His union with the Church was brought about.
Reply to Objection 3. Just as marriage is one on the part of the object to which the union is directed, whereas it is more than one on the part of the persons united, so too the consent is one on the part of the thing consented to, namely the aforesaid union, whereas it is more than one on the part of the persons consenting. Nor is the direct object of consent a husband but union with a husband on the part of the wife, even as it is union with a wife on the part of the husband.
Source: Summa Theologica (New Advent)