This study identified the amino acid sequences of peptides generated from the enzymatic hydrolysis of goat milk proteins from two different sources and annotated their functional activities. Peptidomics and molecular docking approaches were used to investigate the antioxidant and ACE inhibitory properties of the unique peptides, revealing the molecular mechanisms underlying their bioactivity. In vitro experiments showed that the IC50 values for ACE inhibition of the four peptides (LSMTDTR, QEALELIR, NIPVGILR, and QAQNVQHY) were 2.087, 7.584, 2.845, and 4.884 mg/mL, respectively, while the IC50 values for DPPH radical scavenging were 4.466, 4.496, 4.626, and 3.875 mg/mL, respectively, indicating strong antioxidant and ACE inhibitory potential. These findings suggest that goat milk protein could serve as a promising natural source of bioactive peptides with therapeutic potential for managing oxidative stress and hypertension.