In this article, we have developed a computational model to determine the droplet formation regime and its transition in a square microfluidic flow-focusing device that eventually dictate the droplet shape, size, and its formation frequency. We have methodically explored the influences of various physicochemical parameters on the droplet dynamics and flow regime transition, which are essential in the development of new methods for on-demand droplet generation. On the basis of the droplet formation mechanism, we have formulated flow maps for different liquid-liquid systems, and have also proposed a scaling law to predict the droplet length for a wide range of operating condition resulting from the variation of flow rates, and viscosities of the continuous phase as well as the interfacial tension. This work can effectively contribute in providing helpful guidelines on the design and operations of droplet-based flow-focusing microfluidic systems.