Mediterranean countries are known for their high-quality olives and the production and consumption of olive oil. Olive pomace (OP), the major by-product of olive oil extraction, is receiving attention for its potential as a functional compound in food products, reflecting its physiology- and health-promoting attributes. This study assessed the physico-chemical characteristics of OP obtained from two Sardinian olive cultivars, Bosana and Semidana, and the effect of OP incorporation on the baking performance of wheat dough. We assessed the rheological parameters, pasting profile, and fermentation of doughs obtained through the partial substitution of wheat flour with OP at 0 (control), 1, 2, 3, and 5%. OP inclusion resulted in significant differences in the studied parameters compared with control samples. Positive effects included a decrease in development time, improved dough stability and storage, and superior loss modulus and gas retention capacity. Negative effects comprised an increase in dough resistance and a decrease in dough development height, gas production, gas retention, pasting profile, stickiness, and elasticity. These differences in the OP dough were due to the interactions between polyphenols and fibre with water and the starch–gluten matrix. This study found improvements in dough characteristics following the substitution of wheat flour with low percentages of OP, especially Semidana at 1%. Although higher percentages of OP would be associated with greater nutritional and health benefits, they resulted in a degradation of the dough’s attributes, producing a gluten-free-like matrix in the final product.