Parashas Eikev · Passuk 8:10
When you have eaten your fill, give thanks to the ETERNAL your God for the good land given to you.
Torah Temimah points to Arakhin 4a.
TT lemma: ואכלת ושבעת וברכת (unit 4 of 14).
English: It was taught: All are obligated in zimmun, even kohanim. Is that not obvious? It was needed for the case where they eat sacrificial meat: one might have thought this is only kapparah (atonement), not ordinary eating — the verse “you shall eat and be satisfied” teaches that since they do eat and are satisfied, they must bless. This line of thought also supports Birkat HaMazon even outside the Land: the essence is thanks for bodily satiety.
Custom (kohanim eating kodashim; Birkat HaMazon everywhere)
Even eating of sacrificial portions counts as “eating and being satisfied” for the blessing; the obligation is not limited to produce of the Land alone.