The aim of the study was to investigate the effect of using various by-products (orange and apple pomace, tomato peel, pepper peel, prickly pear peel, and prickly pear seed peel) on the dough rheology and properties of gluten-free bread. The by-products were incorporated into a gluten-free bread formulation based on corn and chickpea flours (2/1 w/w). Different levels of each by-product (0, 2.5, 5, and 7.5% in the basic replacement) were tested. Wheat bread and gluten-free bread without the addition of by-products were used as controls. The results indicated that the by-products increased the maximum dough height, the total CO2 production, and CO2 retention coefficient compared to unenriched gluten-free dough. The highest K-value consistency coefficient was observed for the dough enriched with the prickly pear peel. The addition of by-products significantly improved (p < 0.0001) the specific volume of gluten-free bread, with values increasing from 1.48 to 2.50 cm3/g. The hierarchical cluster analysis and the constellation plot showed four groups: the wheat bread group, the second group containing the gluten-free control bread, the group with bread enriched by pomace, and the group with bread enriched with peels, exhibit the same effect on gluten-free bread and the peels exhibit the same effect on gluten-free bread.