Who first clearly formulated the penal substitution theory of atonement? The Wikipedia article on Penal substitution states in its opening paragraph:


  Penal substitution (sometimes, esp. in older writings, called forensic theory) is a theory of the atonement within Christian theology, developed with the Reformed tradition. It argues that Christ, by his own sacrificial choice, was punished (penalised) in the place of sinners (substitution), thus satisfying the demands of justice so God can justly forgive the sins. It is thus a specific understanding of substitutionary atonement, where the substitutionary nature of Jesus' death is understood in the sense of a substitutionary punishment. (italics added)


In the final paragraph of the Overview section, it states further:


  While penal substitution shares themes present in many other theories of the atonement, penal substitution is a distinctively Protestant understanding of the atonement that differs from both Roman Catholic and Eastern Orthodox understandings of the atonement. Many trace its origin to Calvin, but it was more concretely formulated by the Reformed theologian Charles Hodge. Traditionally a belief in penal substitution is often regarded as a hallmark of the evangelical faith and is included as an article of faith by many (but not all) evangelical organizations today. (italics added)


These quotes place the development of penal substitution firmly within the Protestant tradition. However, they, and the article as a whole, are not very conclusive about exactly where and when penal substitution theory originated. Its formulation is attributed to figures as distant from one another in time as John Calvin (1509-1564) and Charles Hodge (1797-1878).

Manwe Elder's answer to my earlier related question, "When and where does the statement, "Christ paid the penalty for our sins" first appear?" does a fine job of briefly tracing the history of the idea of Christ paying the penalty for our sins, and showing that it was not present among major theologians before the Protestant Reformation. It also provides some examples of early Protestant theologians who spoke of Christ paying the penalty for our sins.

A related question of mine also asks, "Did Martin Luther teach penal substitution?"

Given that penal substitution is a distinctly Protestant doctrine (this question is not about earlier foreshadowings or bases of the theory):

What Protestant theologian or theologians first clearly formulated the doctrine of penal substitution?

Whatever other sources an answer may use, please provide direct quotations from the relevant theologians' own writings to support the answer.
Hard to choose, but probably Martin Luther. Your linked answer has the clearest example, from Luther's Works, Volume 26 (Lectures on Galatians Ch. 1-4).


  He sent His Son into the world, heaped all the sins of men upon Him, and said to Him: "Be Peter the denier; Paul the persecutor, blasphemer, and assaulter; David the adulterer; the sinner who ate the apple in Paradise; the thief on the cross. In short, be the person of all men. And see to it that You pay and make satisfaction for them....Whatever sins I, you, and all of us have committed or may commit in the future,
  they are as much Christ’s own as if He Himself had committed them.


However, this is from a 1535 lecture, and so it's not the earliest instance, per se.

In 1530, penal substitution was officially proclaimed as part of the Lutheran faith by the Augsburg Confession at the Diet of Ausburg. (Note the similar phrasing.)


  Also they teach that men cannot be justified before God by their own strength, merits, or works, but are freely justified for Christ's sake, through faith, when they believe that they are received into favor, and that their sins are forgiven for Christ's sake, who, by His death, has made satisfaction for our sins.


Luther approved a draft of the confession, so it's likely that he supported this view of the of atonement by this time, if not earlier.

Around the same time, John Calvin wrote Institutes of the Christian Religion, which was published in 1536.


  He offered in sacrifice the flesh which he took from us, that by expiation wought he might destroy our guilt and appease the Father's just anger.




It's hard to say who had the idea first. Given that Protestantism relied especially on Paul's works, and this interpretation is best supported by him ("For he hath made him to be sin for us"), it's not surprising that Protestant theologians arrived at this doctrine readily.