The production of craft cheeses from goat milk in small farms in Ukraine is becoming increasingly widespread. The uniqueness of goat cheeses made from raw milk is attributed to the significant diversity of microbiological processes that occur during their ripening, involving natural strains of bacteria, fungi, yeasts, and cheese mites. Therefore, this research aimed to determine the microbial composition of Caciotta and Canestrato goat cheeses during their ripening process. The number of mesophilic aerobic and facultative anaerobic microorganisms (MAFAM) in Caciotta cheese was stable on the 10th day, the 1st, and the 12th month, and decreased by 1.18–1.27 lg CFU/g by the 24th month of ripening. The number of mold fungi and yeasts in Caciotta cheese peaked in the 1st month but they were not detected in the 12th and 24th months of ripening. Lactic acid bacteria in Caciotta cheese formed the basis of MAFAM and were represented by Lactobacillus plantarum on the 10th day and the 1st month of ripening, Lactobacillus brevis and Leuconostoc pseudomesenteroides in the 12th month, and L. brevis and Leuconostoc mesenteroides in the 24th month. In 24-month-ripened Caciotta cheese, Escherichia coli, Enterobacter ludwigii, E. durans, E. faecalis, and E. hirae were detected. Lactic acid bacteria in Canestrato cheese formed the basis of MAFAM and were represented by L. mesenteroides from the 10th day to the 3rd month of age, L. pseudomesenteroides in the 6th month, and L. plantarum in the 12th month. Canestrato cheese was characterized by a significant presence of mold fungi and yeasts in all ripening periods except for the 6th month. In 12-month-ripened Canestrato cheese, Enterobacter cloacae, Bacillus cereus, Enterococcus durans, E. hirae, and E. faecalis were isolated. Cheese mites, Acarus siro, in various stages of development were found in the rind of both cheeses starting from the 6th month of ripening. The results of the researchers provide new data on the microbiome of craft hard cheeses made from raw goat milk and can be used to develop methods for controlling the population size of A. siro mites during their ripening.