Pseudomorphic mineral replacement reactions involve one mineral phase replacing another, while preserving the original mineral's size and texture. Macroscopically, these transformations are driven by system-wide equilibration through dissolution and precipitation reactions. It is unclear, however, how replacement occurs on the molecular scale and what role dissolved ion transport plays. Here, we develop a new quantitative framework to explain the pseudomorphic replacement of KBr crystal in a saturated KCl solution through a combination of microscopic, spectroscopic, and modeling techniques. Our observations reveal that pseudomorphic mineral replacement (pMRR) is transport-controlled for this system and that convective fluid flows, caused by diffusioosmosis, play a key role in the ion transport process across the reaction-induced pores in the product phase. Our findings have important implications for understanding mineral transformations in natural environments and suggest that replacement could be exploited in commercial and laboratory applications.