Phase-separated biomolecular condensates often appear as micron-sized droplets. Due to interfacial tension, the droplets usually have a spherical shape and, upon deformation, tend to recover their original shape. Likewise, interfacial tension drives the fusion of two droplets into a single spherical droplet. In all previous studies on shape dynamics, biomolecular condensates have been modeled as purely viscous. However, recent work has shown that biomolecular condensates are viscoelastic, with shear relaxation occurring not instantaneously as would in purely viscous fluids. Here we present an exact analytical solution for the shape recovery dynamics of biomolecular droplets, which exhibits rich time dependence due to viscoelasticity. For condensates modeled as purely viscous, shape recovery is an exponential function of time, with the time constant given by the “viscocapillary” ratio, i.e., viscosity over interfacial tension. For viscoelastic droplets, shape recovery becomes multi-exponential, with shear relaxation yielding additional time constants. The longest of these time constants can be dictated by shear relaxation and independent of interfacial tension, thereby challenging the currently prevailing viscocapillarity-centric view derived from purely viscous fluids. These results highlight the importance of viscoelasticity in condensate shape dynamics and expand our understanding of how material properties affect condensate dynamics in general, including aging. The analytical solution presented here can also be used for validating numerical solutions of fluid-dynamics problems and for fitting experimental and molecular simulation data.