The dispersion and sedimentation of volcanic ash (i.e., tephra with diameter 2 mm) represents a significant threat to many economic sectors and transport infrastructures (e.g., aviation, road network). Several field observations have shown that volcanic ash particles often sediment collectively in the form of aggregates and/or within ash fingers generated by settling‐driven gravitational instabilities (SDGIs). Both processes have a similar impact on tephra fallout by increasing the settling velocities of fine ash (tephra particles 63 microns), causing their premature sedimentation. However, despite having been reported to occur simultaneously during volcanic eruptions, the interactions between these processes have not yet been quantified. We have developed a 3D model that couples a Lattice Boltzmann scheme with a Weighted Essentially Non Oscillatory finite difference scheme and the Smoluchowski coagulation equation that reveals the presence of mutual interactions between aggregation and SDGIs. Indeed, aggregation tends to enhance the sedimentation rate associated with SDGIs which in turn transports aggregates faster to the ground. We also show that the formation of low‐density aggregates such as particle clusters is the most efficient process to remove fine ash prematurely from the volcanic cloud. Failing to describe such interactions can increase the uncertainty of ash dispersal and sedimentation modeling outcomes, especially in the case of ash‐rich volcanic plumes and clouds.