The Sefas Emes zy”a understands the pasuk to mean that after one eats and is satisfied, he naturally comes to bless Hashem. The Gemara (Brachos 35A) says that it is a “svara” (logical conclusion) that one may not derive enjoyment from this world without making a bracha. Thus, it is natural that one automatically blesses Hashem after eating.
He adds that eating provides a person with a spiritual arousal to bless Hashem. Thus, the pasuk is saying that after one eats, he is aroused to bless Hashem.