Ramban

SPEAK UNTO AARON AND UNTO HIS SONS, SAYING: THUS YE SHALL BLESS. I have already mentioned in Seder Vayehi Bayom Ha’shemini, 22. that He commanded Aaron to lift up his hands towards the people and bless them on that day [i.e., the eighth day of the initiation of the priests, which was the day of the final erection of the Tabernacle], and here He commanded Aaron and his sons to do so throughout the generations, and He explained what the blessing was with which they are to bless them. He mentioned this blessing in connection with the setting up of the Tabernacle [discussed in the next chapter], for there the Eternal commanded the blessing, even life forever, just as our Rabbis have said: “In the Sanctuary [the priests pronounced the blessing] using the Divine Name [i.e., the Tetragrammaton], but in the provinces by a substitute Name. In the Sanctuary they pronounced it as a single blessing, but in the provinces [it was pronounced] as three blessings” [the people responding “Amen” to each of the three verses which comprise the priestly blessing], for the blessing in the Sanctuary was singled out by being pronounced with the Proper Name of G-d [i.e., the Tetragrammaton].