It is customary to recite each morning toward the end of the Pesukeh De’zimra service, just prior to the section of Va’yebarech David, four verses from Tehillim that begin with the word "Baruch":
1) "Baruch Hashem Le’olam Amen Ve’amen" (Tehillim 89:53)
2) "Baruch Hashem Mi’Siyon Shochen Yerushalayim Haleluy-a" (Tehillim 135:21)
3) "Baruch Hashem Elokim Elokeh Yisrael Oseh Nifla’ot Lebado" (Tehillim 72:18)
4) "U’baruch Shem Kebodo Le’olam Ve’yimaleh Chebodo Et Kol Ha’aretz Amen Ve’amen" Tehillim 72:19)
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in his work Od Yosef Haim (Parashat Vayigash 13; listen to audio recording for precise citation), explains the reason behind this recitation. He writes that these four verses correspond to the four letters of the Divine Name of "Havaya." The first verse corresponds to the letter Yod at the beginning of this Divine Name, which signifies the Sefira (emanation) of Hochma. The second verse corresponds to the second letter in this Name – the first Heh – which represents Bina. The third verse corresponds to the letter Vav, which alludes to the Sefira of Tiferet, and the fourth verse corresponds to the Name’s final letter, the second Heh, which expresses Malchut, the lowest of the Sefirot. Indeed, as the Ben Ish Hai notes, the fourth verse we recite makes mention of Malchut – "U’baruch Shem Kebod Malchuto" – because it corresponds with that Sefira.
The Ben Ish Hai also comments that the four letters of the word "Baruch," with which each of these verses begins, also correspond to the four letters of the Divine Name of "Havaya."
On the basis of this analysis, the Ben Ish Hai explains why we recite the verses out of sequence. The final two of these four verses are taken from Psalm 72, and we thus might have intuitively expected for them to be recited before the first two verses, which are taken from, respectively, Psalm 89 and Psalm 135. But once we realize that each of these verses corresponds to a different letter of "Havaya," we immediately understand that they must be recited in the sequence corresponding to the spelling of this Divine Name. The sequence of this recitation thus reflects the spelling of "Havaya," and not the sequence of these verses in the Book of Tehillim.
The Ben Ish Hai adds in this context a comment about the phrase "Amen Ve’amen," which appears twice in this series of verses. The word "Amen," he explains, is said to affirm the truth of what had just been recited – in this case, it affirms the truth of "Baruch Hashem Le’olam," that God is eternally blessed. "Amen" is repeated in these verses, the Ben Ish Hai writes, because we affirm God’s stature of greatness both in this world and in the next world. Therefore, the Ben Ish Hai concludes, it is proper when reciting "Amen Ve’amen" in these verses to have in mind that we affirm the truth of God’s dominion both in our world and in the world to come.
Summary: It is customary to recite the four verses of "Baruch Hashem Le’olam" before Va’yebarech David, and these four verses correspond to the four letters of the Divine Name of "Havaya." When reciting the words "Amen Ve’amen" in these verses, one should have in mind that he affirms that God is the exclusive ruler both in this world and the next.
