The aim of this study was to determine the effect of heat treatment of edible insects on antioxidant and anti-inflammatory activities of peptide fractions from hydrolysates obtained by in vitro gastrointestinal digestion thereof. Identification of bioactive peptides from the edible insects and their chemical synthesis were carried out as well. The highest antiradical activity against ABTS•+ and DPPH• was noted for the peptide fraction from the Gryllodes sigillatus protein preparation (EC50 value 2.75 and 6.91 μg mL−1, respectively). This fraction exhibited the strongest LOX and COX-2 inhibitory activity (IC50 value 0.13 and 0.26 μg mL−1, respectively). The peptide fraction from the Tenebrio molitor protein preparation showed the highest Fe2+ chelating ability (EC50 value 2.21 μg mL−1) and the highest reducing power (0.198). The heat treatment process has a positive effect on the antioxidant and anti-inflammatory properties of peptides. All identified and synthesised peptides from insect protein showed antioxidant and anti-inflammatory activity.