33. He now shews a difference between the Law and the Gospel, for the Gospel brings with it the grace of regeneration: its doctrine, therefore, is not that of the letter, but penetrates into the heart and reforms all the inward faculties, so that obedience is rendered to the righteousness of God.
A question may however be here moved, Was the grace of regeneration wanting to the Fathers under the Law? But this is quite preposterous. What, then, is meant when God denies here that the Law was written on the heart before the coming of Christ? To this I answer, that the Fathers, who were formerly regenerated, obtained this favour through Christ, so that we may say, that it was as it were transferred to them from another source. The power then to penetrate into the heart was not inherent in the Law, but it was a benefit transferred to the Law from the Gospel. This is one thing. Then we know that this grace of God was rare and little known under the Law; but that under the Gospel the gifts of the Spirit have been more abundantly poured forth, and that God has dealt more bountifully with his Church. But still the main thing is, to consider what the Law of itself is, and what is peculiar to the Gospel, especially when a comparison is made between the Law and the Gospel. For when this comparison ceases, this cannot be properly applied to the Law; but with regard to the Gospel it is said, that the Law is that of the letter, as it is called elsewhere, (Rom. 7:6;) and this also is the reason why Paul calls it the letter in 2 Cor. 3:6, “the letter killeth,” &c. By “letter” he means not what Origen foolishly explained, for he perverted that passage as he did almost the whole Scripture: Paul does not mean there the simple and plain sense of the Law; for he calls it the letter for another reason, because it only sets before the eyes of men what is right, and sounds it also in their ears. And the word letter refers to what is written, as though he had said, The Law was written on stones, and was therefore a letter. But the Gospel—what is it? It is spirit, that is, God not only addresses his word to the ears of men and sets it before their eyes, but he also inwardly teaches their hearts and minds. This is then the solution of the question: the Prophet speaks of the Law in itself, as apart from the Gospel, for the Law then is dead and destitute of the Spirit of regeneration.
He afterwards says, I will put my Law in their inward parts. By these words he confirms what we have said, that the newness, which he before mentioned, was not so as to the substance, but as to the form only: for God does not say here, “I will give you another Law,” but I will write my Law, that is, the same Law, which had formerly been delivered to the Fathers. He then does not promise anything different as to the essence of the doctrine, but he makes the difference to be in the form only. But he states the same thing in two ways, and says, that he would put his law in their inward parts, and that he would write it in their hearts. We indeed know how difficult it is that man should be so formed to obedience that his whole life may be in unison with the Law of God, for all the lusts of the flesh are so many enemies, as Paul says, who fight against God. (Rom. 8:7.) As then all our affections and lusts thus carry on war with God, it is in a manner a renovation of the world when men suffer themselves to be ruled by God. And we know what Scripture says, that we cannot be the disciples of Christ, except we renounce ourselves and the world, and deny our own selves. (Matt. 6:24; Luke 14:26, 27.) This is the reason why the Prophet was not satisfied with one statement, but said, I will put my Law in their inward parts, I will write it in their hearts.
We may further learn from this passage, how foolish the Papists are in their conceit about free-will. They indeed allow that without the help of God’s grace we are not capable of fulfilling the Law, and thus they concede something to the aid of grace and of the Spirit: but still they not only imagine a co-operation as to free-will, but ascribe to it the main work. Now the Prophet here testifies that it is the peculiar work of God to write his Law in our hearts. Since God then declares that this favour is justly his, and claims to himself the glory of it, how great must be the arrogance of men to appropriate this to themselves? To write the Law in the heart imports nothing less than so to form it, that the Law should rule there, and that there should be no feeling of the heart, not conformable and not consenting to its doctrine. It is hence then sufficiently clear, that no one can be turned so as to obey the Law, until he be regenerated by the Spirit of God; nay, that there is no inclination in man to act rightly, except God prepares his heart by his grace; in a word, that the doctrine of the letter is always dead, until God vivifies it by his Spirit.
He adds, And I will he to them a God, and they shall be to me a people. Here God comprehends generally the substance of his covenant; for what is the design of the Law, except that the people should call upon him, and that he should also exercise a care over his people? For whenever God declares that he will be our God, he offers to us his paternal favour, and declares that our salvation is become the object of his care; he gives to us a free access to himself, bids us to recumb on his grace, and, in short, this promise contains in itself everything needful for our salvation. The case is now also at this day the same under the Gospel; for as we are aliens from the kingdom of heaven, he reconciles us by it to himself, and testifies that he will be our God. On this depends what follows, And they shall be my people; for the one cannot be separated from the other. By these words then the Prophet briefly intimates, that the main object of God’s covenant is, that he should become our Father, from whom we are to seek and expect salvation, and that we should also become his people. Of these things there is more to be said again; but I have explained the reason why I now so quickly pass over things worthy of a longer explanation. 
33 The character of this new covenant is described as one that will be made “after those days” (NASB), referring back to v. 31a and possibly back to v. 27 or even earlier and apparently meaning after they have been planted again in the land (cf. Metsudat David, “after they return from exile”). Interestingly, reference is made here only to the house of Israel, but this must certainly be understood inclusively as referring to both Israel and Judah (mentioned in vv. 29, 31); it may also reflect the fact that the Sinaitic covenant was made with one people, Israel, before there was such a thing as the northern and southern kingdoms. In the same way this new covenant will be made with one people, Israel (cf. esp. 1 Ki 18:31; see also Holladay with reference to Eze 39:15–17).
In this new covenant God’s tôrâ (“teaching, law”) will be put within his people (beqirbām, lit., “in their midst/interior”; the NIV’s “in their minds” is too interpretive) and will be written on their hearts, in obvious contradistinction to the Sinaitic covenant, which was written on tablets of stone (Ex 24:12; 34:1, 4, 28; Dt 4:13; 5:22; 9:9–11; 10:1, 3; see Eze 36:26–27; 2 Co 3:3; cf. further Pss 40:8; 51:6, 10; note Dt 10:16; Jer 4:3–4). Thus it will become Israel’s very nature to keep the commandments of the Lord as their automatic, natural response; this is expressed more fully in the (clearly parallel) new heart passage in Ezekiel 36:26–27, as well as in Jeremiah 32:37–42 (see discussion there; cf. also Eze 11:17–20).
On a practical level, this means that what the psalmist experienced on a temporary and individual level in Psalm 40—delighting in God’s will and having the Torah in his heart before being overwhelmed by the consciousness of his still-present sins—will become Israel’s experience on a corporate and permanent level. Because there will be harmony between Yahweh and his people, the covenantal promise expressed first in Jeremiah in 7:23 and repeated again in 11:1–4 will finally become the reality. As Keil notes, “the essential element of the new covenant, ‘I will be their God, and they shall be my people,’ was set forth as the object of the old; cf. Lev 26:12 with Ex 29:45,” but it is only through the new covenant that it will be realized. As Heschel, 1:128–29, observes, “Prophecy is not God’s only instrument. What prophecy fails to bring about, the new covenant will accomplish: the complete transformation of every individual.” For a thorough interpretive study, see Fẹmi Adeyẹmi, The New Covenant Torah in Jeremiah and the Law of Christ in Paul (Studies in Biblical Literature 94; New York: Peter Lang, 2008).
31:33 I will make: The new covenant would be initiated by God Himself, assuring its effectiveness. after those days: This expression looks forward to the time of fulfillment of the New Covenant, which found fruition in the life, death, and resurrection of Jesus Christ. put My law in their minds … write it on their hearts: Together the mind and heart describe the total inner motivations of mind, will, emotion, and spirit.
31:33 Rather than writing the law on tablets and scrolls (see Ex. 34:1; Deut. 31:9–13) and asking the people to internalize it (Deut. 6:4–9), God will write it on their hearts from the start. He will be the God of this new covenant, just as he was for the old covenant partners who loved him. In Rom. 11:27, Paul takes the words “this will be my covenant with them” from this verse.
31:33 Under the old covenant, the law of God was engraved on tablets of stone and placed in the Most Holy Place; under the new covenant God will write His law on the hearts of His people. The people then are like the temple in that the law of God is within them, but with the difference that they are a living temple, made of living stones (2 Cor. 3:3; 1 Pet. 2:5). See “God’s Covenant of Grace” at Gen. 12:1.
after those days. The prophet speaks of a time after exile, without being specific. The New Testament shows that the time arrived with Christ, the Messiah.
I will. God will take the initiative to renew His people.
my law. The law of Moses required obedience from the heart (Deut. 6:6) but provided no enablement for that obedience (Deut. 5:29; 29:4). It did mediate forgiveness and hope, especially through the sacrifices. The law was a system of “types and shadows,” that is, of significant elements foreshadowing Christ and inviting trust in God through Him.
I will be their God, and they … my people. This declaration is the summary of God’s blessings promised in His covenant (Lev. 26:12; cf. 7:23).
31:33 There are some marked differences between the old and new covenants (v. 32; cf. Gen. 9:13). (1) The Sinai covenant demanded obedience, while the new covenant offers forgiveness of sin. (2) The old covenant was written on stone tablets, while the new covenant is carved on the hearts of God’s people (cf. Ezek. 36:26, 27). (3) The old covenant was between God and the nation Israel, whereas the new covenant is between God and all believers. At the foundation of the new covenant is the fact that God is everything; He will make His people what they ought to be. This new covenant clearly is applicable to two distinct groups. The author of Hebrews recognizes certain fulfillment in those who are saved in the present dispensation (Heb. 8:7–13). However, the covenant as prophesied by Jeremiah must also see a fulfillment in national Israel during the millennial age. The connection between these double fulfillments is actually that of an extension. The new covenant came into force with the atoning death of Christ. All believers in the present church age are the recipients of its benefits. Eventually those benefits will also be extended to include a repentant and regenerate Israel (Rom. 11:25–29).
 Calvin, J., & Owen, J. (2010). Commentaries on the Prophet Jeremiah and the Lamentations (Vol. 4, pp. 130–133). Bellingham, WA: Logos Bible Software.
 Sproul, R. C. (Ed.). (2005). The Reformation Study Bible: English Standard Version (p. 1099). Orlando, FL; Lake Mary, FL: Ligonier Ministries.
 Criswell, W. A., Patterson, P., Clendenen, E. R., Akin, D. L., Chamberlin, M., Patterson, D. K., & Pogue, J. (Eds.). (1991). Believer’s Study Bible (electronic ed., Je 31:33). Nashville: Thomas Nelson.