You can look at the Catechism of the Catholic Church for more information about equating the moral law with the Ten Commandments.

Here you can read a nice summary of this section. But, to break it up into some parts to help explain, you may want to look at the definition of a moral law:

• 1950 The moral law is the work of divine Wisdom. Its biblical meaning can be defined as fatherly instruction, God's pedagogy. It prescribes for man the ways, the rules of conduct that lead to the promised beatitude; it proscribes the ways of evil which turn him away from God and his love. It is at once firm in its precepts and, in its promises, worthy of love.
• 1952 There are different expressions of the moral law, all of them interrelated: eternal law - the source, in God, of all law; natural law; revealed law, comprising the Old Law and the New Law, or Law of the Gospel; finally, civil and ecclesiastical laws.
• 1953 The moral law finds its fullness and its unity in Christ. Jesus Christ is in person the way of perfection. He is the end of the law, for only he teaches and bestows the justice of God: "For Christ is the end of the law, that every one who has faith may be justified."

So, the first stage of revealed law is the Ten Commandments, but these were perfected by the New Law (the grace of the Holy Spirit), so we can see by the CCC that moral law is more than just the Ten Commandments, but, also covers the New Law.

Now, as much as I am a huge fan of Aquinas, I tend to think that there can be problems with his divisions, but they can also be useful for explanation, but the problems should also be understood.

This article does a good job of explaining problems with dividing them.

We should not decide which is critical to obey and which can be ignored, safely. I like this quote from the link above:

If God says it, it is immoral to disobey. Morality is not a standard independent of God. God decides what is right and what is wrong.

Here is a likely reason for the three-part division, taken from this historical background:

Why were the dogmatical terms of Moral, Civil and Ceremonial developed if there is no division in the Bible and the Jews never considered the Law as threefold? The division probably was developed because there are 3 natural parts to the Mosaic Law. It also makes for easier teaching when we study the Old Testament Law in a threefold sense. The Law of Moses is massive in scope.

So, you are correct that it appears to have started with Aquinas, as far as I can tell, but there does seem to be a natural split of the Law into two parts, a moral and ceremonial, as well.

Division of the law in the early church

The law has been "divided" since the early church, but at first only into two parts. Justin Martyr, Irenaeus, Augustine, and others described a distinction between what we know as the moral law and the ceremonial/civil law, and connected the moral law with the ten commandments. For example, Irenaeus argues that the "laws of bondage," which have been "cancelled by the new covenant,"¹ were only added to the ten commandments following the incident with the golden calf:

As Moses says in Deuteronomy, “These are all the words which the Lord spake to the whole assembly of the sons of Israel on the mount, and He added no more; and He wrote them on two tables of stone, and gave them to me.” [Deut. 5:22] For this reason (He did so), that they who are willing to follow Him might keep these commandments. But when they turned themselves to make a calf, and had gone back in their minds to Egypt, desiring to be slaves instead of free-men, they were placed for the future in a state of servitude suited to their wish,—(a slavery) which did not indeed cut them off from God, but subjected them to the yoke of bondage; as Ezekiel the prophet, when stating the reasons for the giving of such a law, declares: “And their eyes were after the desire of their heart; and I gave them statutes that were not good, and judgments in which they shall not live.” [Ezek. 20:24–25]²

Augustine argues similarly, calling the two parts of the law "moral" and "symbolic," and says that "it is no longer necessary to continue the symbolical observances":

For example, "Thou shalt not covet" is a moral precept; "Thou shalt circumcise every male on the eighth day" is a symbolical precept.³

Tripartite division

All this said, historians typically credit Aquinas with the origin of the tripartite, or threefold, division of the law. J. V. Fesko says that "Aquinas is often credited with formalizing the threefold distinction,"⁴ and Harold Cunningham calls him the "father of the scheme."⁵ Aquinas lays out the now-common division as follows:

We must therefore distinguish three kinds of precept in the Old Law; viz. "moral" precepts, which are dictated by the natural law; "ceremonial" precepts, which are determinations of the Divine worship; and "judicial" precepts, which are determinations of the justice to be maintained among men.⁶

One passage he uses to defend this threefold division is Deuteronomy 6:1:

It is written: "These are the precepts and ceremonies, and judgments": where "precepts" stands for "moral precepts" antonomastically. Therefore there are judicial precepts besides moral and ceremonial precepts.⁶

As for the biblical association between the ten commandments and the moral law, Aquinas adds to the passages mentioned by Irenaeus above (Deuteronomy 5:22, Ezekiel 20:24–25), quoting Deuteronomy 4:13–14:

It is written: "Ten words . . . He wrote in two tables of stone; and He commanded me at that time that I should teach you the ceremonies and judgments which you shall do." But the ten commandments of the Law are moral precepts. Therefore besides the moral precepts there are others which are ceremonial.⁷

The reformers did widely adopt the same scheme – a few centuries after Aquinas, Calvin calls the threefold distinction "well known," attributes it to the "ancients," and does not provide an extensive biblical defense:

We must attend to the well known division which distributes the whole law of God, as promulgated by Moses, into the moral, the ceremonial, and the judicial law, and we must attend to each of these parts, in order to understand how far they do, or do not, pertain to us.⁸

Summary

Aquinas is widely regarded as the first to posit and defend a threefold distinction of the law – moral, ceremonial, and civil. His division is a development from the division maintained in Augustine and other church fathers, in which the moral law is distinguished from the parts of the law that have passed away in the new covenant. And following him were many reformers, such as John Calvin and the Westminster Divines, who likewise held a tripartite division of the law.

In addition to the references below, Stephen J. Casselli's article, "The Threefold Division of the Law in the Thought of Aquinas", is helpful and detailed in its analysis of the thinkers that influenced Aquinas and his view of the law.

1. Irenaeus, Against Heresies, 4.16.5
2. Against Heresies, 4.15.1
3. Augustine, Reply to Faustus the Manichaean, 6.2
4. Fesko, The Theology of the Westminster Standards, Chapter 9
5. Cunningham, "God's Law, 'General Equity' and the Westminster Confession of Faith"
6. Aquinas, Summa, First part of the second part, Q99-4
7. Summa, First part of the second part, Q99-3
8. Calvin, Institutes, 4.20.14