Summary: The large-scale injection of carbon dioxide \((CO_{2})\) into saline aquifers is a promising tool for reducing atmospheric \(CO_{2}\) emissions to mitigate climate change. An accurate assessment of the post-injection migration and trapping of the buoyant plume of \(CO_{2}\) is essential for estimates of storage capacity and security, but these physical processes are not fully understood. In Part I of this series [the authors, ibid. 662, 329–351 (2010; Zbl 1205.76255)], we presented a complete solution to a theoretical model for the migration and capillary trapping of a plume of \(CO_{2}\) in a confined, sloping aquifer with a natural groundwater through-flow. Here, we incorporate solubility trapping, where \(CO_{2}\) from the buoyant plume dissolves into the ambient brine via convective mixing. We develop semi-analytical solutions to the model in two limiting cases: when the water beneath the plume saturates with dissolved \(CO_{2}\) very slowly or very quickly (‘instantaneously’) relative to plume motion. We show that solubility trapping can greatly slow the speed at which the plume advances, and we derive an explicit analytical expression for the position of the nose of the plume as a function of time. We then study the competition between capillary and solubility trapping, and the impact of solubility trapping on the storage efficiency, a macroscopic measure of plume migration. We show that solubility trapping can increase the storage efficiency by several-fold, even when the fraction of \(CO_{2}\) trapped by solubility trapping is small.