The objective of this study was to develop an alternative novel process technology for enhancing the rheological and functional properties of Greek-style yogurt (GSY). The GSY was formulated and prepared in the lab using micellar casein concentrate as a source of protein to achieve a protein content of 10% (w/w). The changes in physicochemical, microstructural, rheological, and functional properties of control (C-GSY) and micro- and nano-bubbles-treated GSY (MNB-GSY) were studied and compared before and after storage for 1, 2, 3, and 4 weeks. Before storage, the apparent viscosity at 100 s−1 (η100) was 1.09 Pa·s for C-GSY and 0.71 Pa·s for MNB-GSY. Incorporation of MNBs into GSY significantly (p < 0.05) decreased the η100 by 30% on 1 week of storage. Additionally, the η100 of MNB-GSY was lesser than C-GSY on week 2, 3, and 4 of storage. Notable microstructural changes and significant rheological differences were observed between the C-GSY and MNB-GSY samples. Differences were also noticed in syneresis, which was lower for the MNB-GSY compared with the control. Overall, the incorporation of MNBs into GSY showed considerable improvements in rheological and functional properties. Additionally, it’s a simple, cost-effective process to implement in existing GSY production plants.