Henry's quote is verbatim from Christoph Pezel's 1590 book Außführliche, warhaffte und bestendige Erzehlung, and he mentions Pezel in a footnote to the paragraph prior to the story. Many sources indicate that the story originates with Pezel.
I found a few historians who weighed in on whether the story was credible or not.
Paul Henry says in The Life and Times of John Calvin that the story bears "all the internal signs of truth" and "is wanting in none of the outer."
Julius Kostlin says in Theology of Luther in Its Historical Development and Inner Harmony Part 2 (pg. 191):
Under these circumstances [the cooling of Luther's attitude toward Bucer], there is no internal improbability in the report, that he greeted with rejoicing the tract upon the Lord's Supper which Calvin had meanwhile published, although it is open to question in how far Pezel's account of this incident is trustworthy.
Johann Karl Ludwig Gieseler concludes that the story is credible while discussing a different but related matter in A Text-book of Church History: A.D. 1517-1648 (The Reformation and its Results to the Peace of Westphalia) (pg. 414 n. 43):
As Luther at this time  must have known the Institutions of Calvin, it follows, from the declarations of this letter, that he was then satisfied with his [Calvin's] doctrine upon the Lord's Supper; and, besides, it also fully agreed with that to which the Swiss had declared assent to Luther in 1536. Thus the avowals of Luther about Calvin are trustworthy, given by Christoph. Pezel.
Brian Gerrish hedges on whether the story is reliable, in The Old Protestantism and the New (pg. 286 n. 53):
Mülhaupt ("Luther und Calvin," p. 103) suspects this story of being a mere embellishment of the incident Calvin reported to Farel in his letter of 20 November 1539, where, as we have seen, the writing in question is not identified. But this is mere guess-work, and the story may well be authentic; Pezel relates it with attention to details and also names the witness (one of Luther's table companions) from whom the incident is derived. On the other hand, it is quite plain from two passages in the Table Talk that Luther's attitude toward Calvin in the closing years of his life was a mixture of respect and suspicion: W.A.Tr. 5.51.19 (no. 5303) and 461.18 (no. 6050).
Calvin's letter to Farel and the two Table Talk passages will be discussed briefly below, in the "Luther on Calvin" section.
Rudolph Hospinian also told the story (more briefly) in his History of the Sacraments (1598), though I was only able to find a Latin version and I couldn't locate the story in that edition. Gerrish (on the page quoted above) and Erwin Doumergue say he was an independent reporter, but Gieseler thinks he borrowed it from Pezel. Says Doumergue (Jean Calvin, pg. 573 n. 1):
Hospinian has not borrowed from Pezel because according to his method, he would have cited the main passages verbatim. They probably had two different sources.
It's worth noting also that Pezel was a Lutheran who was under suspicion for much of his life of being a crypto-Calvinist on the sacraments, and Hospinian was Swiss Reformed, so he was either Calvinist or Zwinglian on the sacraments.
Luther on Calvin
Gerrish has elsewhere written an overview of Luther's statements on Calvin, titled "Luther and the Reformed Eucharist: What Luther Said, or Might Have Said About Calvin." James Swan has written a helpful summary of Gerrish's article at his blog post "Luther and Calvin... Friends or Enemies?"
Since Mülhaupt (mentioned above) believed that the incident in question was an embellishment of a claim Calvin makes in a letter to Farel, it makes sense to quote part of Gerrish's treatment of the letter here:
In a letter to Guillaume Farel, dated 20 November 1539, Calvin reports that Luther has asked Bucer to greet his young French associate for him: "Will you pay my respects (salutabis reverenter) to John Sturm and John Calvin. I have read their little books with singular enjoyment." We can forget about John Sturm for the moment. Calvin exclaims with evident delight: "Just think what I say there about the Eucharist! Consider Luther's generosity (ingenuitatem)! It will be easy to decide what reason they have who so obstinately disagree with him." Calvin goes on to say that Philipp Melanchthon has confirmed the good news of Luther's high regard for him, and has instructed the letter-carrier to deliver an oral message, which Calvin reports in these words:
Certain persons, to irritate Martin, pointed out to him the aversion with which he and his followers were alluded to by me. So he examined the passage in question and felt that he was there, beyond doubt, under attack. After a while, he said: "I certainly hope that he will one day think better of us. Still, it is right for us to be a little tolerant toward such a gifted man." We are surely made of stone [Calvin comments] if we are not overcome by such moderation! I, certainly, am overcome, and I have written an apology (satisfactionem) for insertion into my preface to the Epistle to the Romans.
The intriguing question is, of course: What book of Calvin's had Luther read "with singular enjoyment"? ... The case for ... the Reply to Sadoleto, it seems to me, is clinched by the fact that the Luther's request to Bucer—"pay my respects to John Sturm and John Calvin," etc.—is followed immediately by the caustic remark, "As for Sadoleto, I wish he would believe that God is the creator of men even outside of Italy."
Swan's and Gerrish's links also contain a brief discussion of the Table Talk entries on Calvin, among other things.
Note on sources
I am indebted to Nathaniel's answer for its alternate translation, which (via Google) was my gateway to Gerrish, who in turn was my gateway to all the rest of my sources.