Stevia rebaudiana Bertoni is a plant cultivated worldwide due to its use as a sweetener. The sweet taste of stevia is attributed to its numerous steviol glycosides, however, their use is still limited, due to their bitter aftertaste. The transglycosylation of steviol glycosides, aiming at the improvement of their taste, has been reported for many enzymes, however, glycosyl hydrolases are not extensively studied in this respect. In the present study, a β-glucosidase, MtBgl3a, and a β-galactosidase, TtbGal1, have been applied in the transglycosylation of two steviol glycosides, stevioside and rebaudioside A. The maximum conversion yields were 34.6 and 33.1% for stevioside, while 25.6 and 37.6% were obtained for rebaudioside A conversion by MtBgl3a and TtbGal1, respectively. Low-cost industrial byproducts were employed as sugar donors, such as cellulose hydrolyzate and acid whey for TtbGal1- and MtBgl3a- mediated bioconversion, respectively. LC-HRMS analysis identified the formation of mono- and di- glycosylated products from stevioside and rebaudioside A. Overall, the results of the present work indicate that both biocatalysts can be exploited for the design of a cost-effective process for the modification of steviol glycosides.