Did David prophesy "God ruling the nations from a Tree"? A few days ago (on the Feast of the Cross) the Vexilla Regis popped up in the breviary. Its 3rd/4th stanza says:


  That which the prophet-king of old
  hath in mysterious verse foretold,
  is now accomplished, whilst we see
  God ruling the nations from a Tree.  


The prophet-king is obviously the Old Testament King David (the Latin original as well as most translations I found mention him more explicitly).  In the context of the hymn it is clear that this prophecy is foretelling Jesus' death on the cross—his death as the victory establishing his kingdom, the tree as cross he died on.

To me this seems to be a very explicit prophecy made by David. Unfortunately I was not able to find such a prophecy.

Question: Is there any place in the Bible (probably the Psalms) or in the extrabiblical tradition ascribing a similar prophecy to King David? If not, where does the cited piece of the hymn have its origin?
See King David's Psalm 95:10:


  say ye among the Gentiles that our Lord hath reigned*. For he hath corrected the round world which shall not be moved: he will judge peoples in equity.*[Some add here: "from the wood/tree/cross" or "a ligno." See commentary below.]


The Original Douay-Rheims commentary on this verse notes that:


  Diverse ancient Doctors read more in this place: Our Lord hath reigned from the wood [a ligno], to wit, Christ by his death on the cross conquered the Devil, sin, and death, and thence began to reign. St. Justinus Martyr, dialogo aduers. Triphonem. Tertullian li. aduers. Iudæos. c. 9. &amp;. 13.  &amp; aduers Marcionem. li 3 c. 19. &amp;. 21. St. Augustine, in this place, according to the old Roman Psalter Before him Arnobius, and after him Cassiadorus and others, Whereby it is probable, that it was sometimes in the Hebrew text, and blotted out by the Jews.


From the Haydock Commentary:


  Ver. 10. Reigned. St. Bernard says, "the kingdom of Jesus is in the wood." (Du Hamel) --- St. Justin Martyr (Dialogue with Trypho) accuses the Jews of retrenching apo tou xulou, "from the wood," which all the Latin Fathers, except St. Jerome, acknowledge in their copies. That ancient author, being born among the Samaritans, could hardly be so ignorant of the Hebrew text, and his antagonist does not attempt to refute the charge; so that it seems probable, that they were in the original, (Berthier) and since erased by the Jews, from the Septuagint, who added them, (Worthington) by the spirit of prophecy. (Tournemine) --- But how came Christians to permit this to be done in their Hebrew, Greek, and Latin copies? The words in question may have been, therefore, a marginal gloss, which had crept into the text. (Faber, Justiniani, &amp;c.) --- They do not occur in the parallel passage, (1 Paralipomenon) nor in the Vulgate, though they be retained in the Roman breviary. (Calmet) --- Lindan objects this perfidy of the Jews to the Reformers, not reflecting, that he thus condemns the Vulgate. Genebrard is of opinion, that "the Septuagint were inspired to add these words, which some half-learned critics have thought proper to expunge with an impiety which is now but too common." The Popes have not, however, thought that the cross stood in need of this support. (Amama) --- The Chaldean and Syriac, as well as all the copies of the Septuagint extant, and the Arabic and Ethiopic versions taken from it, and all the Greek interpreters and Fathers, (except St. Justin) with St. Jerome, both in his versions from the Hebrew and Septuagint, omit these words, which are found in the Roman, Gothic, and other psalters. Origen's Hexapla seem to have most enabled the Greeks to discern the interpolation, which the Latins retained longer, not having such easy access to that work. Whatever may be the decision on this important matter, it is certain that the reign of Christ was propagated from the wood, in a wonderful manner, as he there began to draw all to himself, and the prophet seems evidently to allude to the times when Christ proclaimed, the kingdom of God is at hand, and when the conversion of the Gentiles, and the institution of the blessed Eucharist (ver. 8.) would fill all the world with rapture. (Haydock) --- The positive testimony of St. Justin, and the Italic version used by the Latin Fathers, (Berthier) Tertullian, St. Augustine, &amp;c., (Worthington) seems of more weight to prove the authenticity of the words, than the simple omission in the copies of Origen, and St. Jerome, &amp;c., to evince the contrary. (Berthier) --- Corrected. Evil morals and idolatry, (Menochius) rather than the physical order of the globe, Psalm xcii. 1. (Berthier) --- Hebrew, "he hath balanced," (Houbigant) or established. (Haydock) --- The Christian faith shall not be abolished, (Menochius) or corrected. (Haydock) --- "Faith is not to be reformed." (Tertullian) --- Justice. Ancient psalters add, "and the Gentiles in his wrath," ver. 13., and Psalm xcviii. 8.


Here is what St. Justin Martyr says (Dialogue with Trypho ch. 73) about the alleged removal of the words "from the wood":


  Justin: And from the ninety-fifth (ninety-sixth) Psalm they have taken away this short saying of the words of David: 'From the wood.' For when the passage said, 'Tell among the nations, the Lord has reigned from the wood,' they have left, 'Tell among the nations, the Lord has reigned.' Now no one of your people has ever been said to have reigned as God and Lord among the nations, with the exception of Him only who was crucified, of whom also the Holy Spirit affirms in the same Psalm that He was raised again, and freed from [the grave], declaring that there is none like Him among the gods of the nations: for they are idols of demons. But I shall repeat the whole Psalm to you, that you may perceive what has been said. It is thus: 'Sing unto the Lord a new song; sing unto the Lord, all the earth. Sing unto the Lord, and bless His name; show forth His salvation from day to day. Declare His glory among the nations, His wonders among all people. For the Lord is great, and greatly to be praised: He is to be feared above all the gods. For all the gods of the nations are demons but the Lord made the heavens. Confession and beauty are in His presence; holiness and magnificence are in His sanctuary. Bring to the Lord, O you countries of the nations, bring to the Lord glory and honour, bring to the Lord glory in His name. Take sacrifices, and go into His courts; worship the Lord in His holy temple. Let the whole earth be moved before Him: tell among the nations, the Lord has reigned. For He has established the world, which shall not be moved; He shall judge the nations with equity. Let the heavens rejoice, and the earth be glad; let the sea and its fullness shake. Let the fields and all therein be joyful. Let all the trees of the wood be glad before the Lord: for He comes, for He comes to judge the earth. He shall judge the world with righteousness, and the people with His truth.'
  
  Trypho: Whether [or not] the rulers of the people have erased any portion of the Scriptures, as you affirm, God knows; but it seems incredible.
  
  Justin: Assuredly, it does seem incredible. For it is more horrible than the calf which they made, when satisfied with manna on the earth; or than the sacrifice of children to demons; or than the slaying of the prophets. But you appear to me not to have heard the Scriptures which I said they had stolen away. For such as have been quoted are more than enough to prove the points in dispute, besides those which are retained by us, and shall yet be brought forward.