The paragraph known to us as "Ashreh," which we recite three times each day (twice during Shaharit and once at Minha), consists of the 145th chapter of Tehillim, and we introduce it with two verses from elsewhere in Tehillim that begin with the word "Ashreh" ("Ashreh Yoshebeh Betecha" – 84:5; "Ashreh Ha'am She'kacha Lo" – 144:15).
This 145th chapter of Tehillim concludes with the verse "Tehilat Hashem Yedaber Pi, Vi'ybarech Kol Basar Shem Kodsho Le'olam Va'ed." However, in our recitation of Ashreh, we add afterward a different verse from Tehillim (115:18) – "Va'anahnu Nebarech Y-ah Me'ata Ve'ad Olam Haleluy-ah."
Rav Amram Gaon (810=-875) explained that we add this verse for the sake of maintaining consistency in the text of Pesukeh De'zimra. The chapters of Tehillim recited as part of this section of the prayer service all conclude with the word "Haleluy-ah," except the chapter of Ashreh. We therefore add this verse so that we conclude even this chapter with the word "Haleluy-ah."
The Bet Yosef questions this explanation, noting that it fails to account for our adding this verse also on the other two occasions when we recite Ashreh – before U'ba Le'sion, and during Minha. In truth, there were those – like the Maharshal (Rav Shlomo Luria, Poland, 1510-1573) – who maintained that "Va'anahnu Nebarech Y-ah" should indeed be added to Ashreh only in Pesukeh De'zimra in the morning. However, the accepted practice is to add it even before U'ba Le'sion and during Minha. It is possible that since we add this verse in Pesukeh De'zimra for the sake of maintaining consistency, it was established that this verse should be added whenever Ashreh is recited.
The recitation of this verse might also be explained in light of the Gemara's teaching (Berachot 4b) that one who recites this chapter of Tehillim three times each day is assured a share in the next world. After reciting this chapter, we add the verse "Va'anahnu Nebarech Y-ah," proudly proclaiming that we will praise Hashem "Me'ata Ve'ad Olam" – for all eternity. As we adhere to the practice of reciting this chapter three times every day, we can confidently declare with excitement and enthusiasm that we will have the privilege of praising Hashem also in the eternal world.