While many today are unaware of it, predestination is an official dogmatic teaching of Catholicism and was elevated to dogma at the Council of Orange (AD 529). Note, for instance, the following canons:
Canon 3: If anyone says that the grace of God can be bestowed by human invocation, but that the grace itself does not bring it to pass that it be invoked by us, he contradicts Isaias the Prophet, or the Apostle who says the same thing: “I was found by those who were not seeking me: I appeared openly to those, who did not ask me” [Rom. 10:20; cf. Isa. 65:1].
Canon4: If anyone contends that in order that we may be cleansed from sin, God waits for our good will, but does not acknowledge that even the wish to be purged is produced in us through the infusion and operation of the Holy Spirit, he opposes the Holy Spirit Himself, who says through Solomon: “Good will is prepared by the Lord” [Prov. 8:35: LXX], and the Apostle who beneficially says: “It is God, who worlds in us both to will and to accomplish according to his good will” [Phil. 2:13].
The Catholic doctrine of predestination is succinctly explained in section 600 of the 1994 Catechism of the Catholic Church:
To God, all moments of time are present in their immediacy. When therefore he establishes his eternal plan of "predestination", he includes in it each person's free response to his grace . . .
Notwithstanding, there remains allowable theological debate and disagreement over some of the “mechanics” of predestination within Catholicism. In his discussion of Catholic sacramental theology, Arthur Devine has a useful discussion about the debate between Thomists and non-Thomists on this issue:
The different systems which Catholic theologians propose on this subject, according to that judicious writer, can be reduced to two principal and fundamental ones, namely, (1) that of those who attribute the efficacy of efficaciousness of graces to the free consent of the will, and (2) that which attributes it entirely to the intrinsic nature of grace itself.
(1) The Molinist or Congruist System—According to this system, that grace is called efficacious to which God saw from all eternity that man would consent, under the circumstances in which it would be given to him. And that grace is called sufficient to which God foresaw from all eternity that man would not consent, although he had he real power to consent under the circumstances in which it would be given. It follows from this, according to the defenders of the system, that one and the same grace would be efficacious in one man, and only sufficient in another; and even with respect to the same individual it would be efficacious in some circumstances, and not under unfavourabe ones. Such, in short, is the system sustained in substance, although with different modifications, by Molina, Suarez, Vasquez, and, for the most part, by the theologians of the Society of Jesus.
(2) The Thomist System, or that of the Dominican School.—According to this, the efficaciousness of grace comes from the intrinsic nature of grace itself. It is the very nature of efficacious grace that, with its aid, the will does good, although, absolutely speaking, under the circumstances it need not do it, and is free not to do it. It is of the nature of sufficient grace that with it the will does not do good, although under the circumstances, and absolutely speaking, it can do it.
In this system we are to recognize from the very nature of efficacious grace a certain and infallible connection between grace and the consent of the will, although by no means a necessary connection. And between sufficient grace and the consent of the will we have to recognize a certain and infallible connection between the grace and the omission of the act for which it is given though this connection must not be regarded as necessary in any sense. It should be noted that this omission is not to be attributed to sufficient grace, but to the bad will of the person who resists it. This system supposes, and rightly supposes, an essential difference between a necessary connection and a certain and infallible connection of a cause with its effect. We can perceive that a cause can have a certain and infallible connection with its effect without it being necessary Daily experience furnishes us with many examples of this.
Thus, for example, a public porter, to whom you offer a sovereign to perform at once some easy commission for you, will certainly and infallibly accept your proposition with great readiness and pleasure, although he does not do so necessarily, and he can, under the circumstances, reuse to oblige you. Again, a good, honest and honourable man or woman will certainly refuse to entertain an unworthy and dishonourable suggestion to do something disgraceful, although that refusal is not the result of necessity. Again, an honest and conscientious judge will certainly and infallible refuse a bribe to commit an injustice. From these examples we can easily understand by mere human knowledge how the certain and infallible determination of the will need not be at all necessary, and that persons who will certainly and infallibly do one thing retain the power of not doing it, or of doing the contrary; otherwise their actions could neither by praiseworthy nor blameable, or as our commonsense tells us. (Arthur Devine, The Sacraments Explained According to the Teaching and Doctrine of the Catholic Church [3d ed.; London: R&T Washbourne, 1905], 37-39)
Elsewhere, we read:
6. All agree to the following propositions which contain a summary of the doctrine of predestination:
(1) There is in God the decree of predestination—that is to say, an absolute and efficacious will to bestow His kingdom on those who in effect will possess it.
(2) God, in predestinating souls to eternal glory, ordains also the means and the graces by which they will infallibly obtain it.
(3) That decree of God is from all eternity, before the foundation of the world.
(4) It is in effect of His pure bounty, and is entirely free on His part.
(5) The decree of predestination is certain and infallible on the part of God, so that it will be most certainly executed, and no obstacle can prevent its execution.
(6) It is uncertain as regards men, so that no one without an express revelation from God can know whether he is of the number of the elect or predestined or not.
(7) The number of the predestined is fixed and immutable, so that it can neither be increased nor diminished, because the decree of God is eternal and His knowledge cannot fail.
(8) The decree of predestination, either by itself or by the means God employs in carrying it out, does not place the elect under any necessity to do good. They act always with perfect freedom, and even when they fulfil the law they have the full power of doing otherwise.
(9) The predestination to grace is absolutely gratuitous, depending solely on the mercy of God, and not on any natural merit on our part.
(10) The predestination to glory is not founded on the foreknowledge of human merits acquired by the sole power of nature and free-will, because no one can be saved except through Jesus Christ.
(11) The actual giving of heaven, or predestination in executione, as it is termed, is granted on account of the merits of grace, as glory is called in the Sacred Scripture the reward, the recompense, and the crown of justice.
Such are the various points of doctrine which are either formally contained in Sacred Scripture or defined by the Church concerning predestination, against the Pelagians, Semipelagians, and the Protestants. They are truths, and not opinions, which theologians are free to hold or to reject.
7. There is, however, a point disputed amongst Catholic schools of theology, namely, as to whether the decree of predestination is in the Divine intention anterior or posterior of the prevision of man’s supernatural merits by the aid of grace. This question is whether, according to our manner of understanding, God wishes in the first place, by an absolute and efficacious will, the salvation of some of His creatures, and if it is in consequence of this will or this decree that He determines to grant them graces which will enable them infallibly to perform good works; or, on the contrary, whether it is that God determines to grant to His creatures all the graces necessary for salvation, and that it is solely in consequence of foreseeing the merits which will result from the good use of His graces that he determines to give them eternal life. In other words, it is a question whether God elects a man to glory either before his merits and foreseen or after the foreseen merits.
Some hold that the decree of predestination is absolute, antecedent, and gratuitous in every respect; others hold that this decree is conditional and consequent, but always gratuitous in the sense that it must suppose merits acquired by gratuitous graces. Let us be satisfied with this simple statement of the two opinions, as we cannot pretend to understand the manner in which God conceives and orders and arranges His decrees. This question was warmly debated at the Council of Trent between the Franciscans and the Dominicans, but the Council wisely abstained from pronouncing any decision on the point, and confined its decision to condemning the excesses and errors of Protestants and other heretics opposed to the Catholic doctrine of predestination. (Ibid., 95-97)
For further reading on the Catholic understanding of predestination, see, for instance:
John Salza, The Mystery of Predestination: According to Scripture, The Church, and St. Thomas Aquinas
William G. Most, Grace, Predestination, and the Salvific Will of God: New Answers to Old Questions
Reginald Garrigou-LaGrange, Predestination: The Meaning of Predestination in Scripture and the Church