Microwell arrays are amongst the most commonly used platforms for biochemical assays. However, the coalescence of droplets that constitute the dispersed phase of suspensions housed within microwells has not received much attention to date. Herein, we study the coalescence of droplets in a two-phase system in a microwell driven by surface acoustic waves (SAWs). The microwell structure, together with symmetric exposure to SAW irradiation, coupled from beneath the microwell via a piezoelectric substrate, gives rise to the formation of a pair of counter-rotating vortices that enable droplet transport, trapping, and coalescence. We elucidate the physics of the coalescence phenomenon using a scaling analysis of the relevant forces, namely, the acoustic streaming-induced drag force, the capillary and viscous forces associated with the drainage of the thin continuous phase film between the droplets and the van der Waals attraction force. We confirm that droplet-droplet interface contact is established through the formation of a liquid bridge, whose neck radius grows linearly in time in the preceding viscous regime and proportionally with the square root of time in the subsequent inertial regime. Further, we investigate the influence of the input SAW power and droplet size on the film drainage time and demarcate the coalescence and non-coalescence regimes to derive a criterion for the onset of coalescence. The distinct deformation patterns observed for a pair of contacting droplets in both the regimes are elucidated and the possibility for driving concurrent coalescence of multiple droplets is demonstrated. We expect the study will find relevance in the demulsification of immiscible phases and the mixing of samples/reagents within microwells for a variety of biochemical applications. © 2021 American Chemical Society.