To meet the demand for new functional foods in line with the trend of sustainable development, a novel probiotic yogurt fortified with 1%, 3%, and 5% apple pomace flour (APF) added immediately after inoculation with Lactobacillus acidophilus, Streptococcus thermophilus, and Bifidobacterium bifidum was developed. Upon fermentation in the presence of APF, a number of probiotic strains remained within the required range, while the syneresis of enriched yogurts was reduced up to 1.8 times in comparison to the control. Supernatants (i.e., extracted whey) obtained from yogurts with 1%, 3%, and 5% APF respectively had 1.4-, 1.8-, and 2.3-fold higher total phenolic content (TPC) than the control, 3.3-, 4.7-, and 8.0-fold higher radical scavenging (DPPH), and 1.3-, 1.6-, and 1.7-fold higher reducing activity (FRAP). Also, probiotic yogurt supernatants (3% and 5%) inhibited colon cancer cells’ viability (HCT 116, 12% and 17%; SW-620, 13% and 19%, respectively). The highest firmness, cohesiveness, and viscosity index values, and the highest scores for color and taste, were obtained for yogurt with 3% APF, indicating that this is the optimal APF amount for the production of novel yogurt with functional properties.