Ocean isotope tracers of intermediate residence time are becoming of increasing importance in studies of paleo‐ocean circulation, global weathering fluxes, and trace pollutant dispersion in ocean basins. While analytical models exist that predict the way in which conservative tracers are dispersed in ocean gyres, the lateral movement of reactive tracers has not yet received much attention. Here we present time‐dependent numerical simulations of the lateral mixing process (advection‐diffusion‐reaction) of reactive tracers with different residence times in gyres with varying Péclet number, diffusivity, western boundary intensification, and source geometry. Our main conclusions are that in our model gyre (1) homogenization of tracer concentrations and also of isotopic ratios in those cases where the isotopes have different pathways (e.g., atmospherically deposited cosmogenic ¹⁰Be, continent‐derived ⁹Be) depends largely on the residence time and eddy diffusivity and is only a weak function of Péclet number; (2) western intensification influences homogenization only in the case of short residence times and large Péclet numbers; (3) homogenization of isotopic ratios of continent‐sourced tracers (e.g., ²⁰⁶Pb/²⁰⁴Pb, ¹⁴³Nd/¹⁴⁴Nd) is favored by high water velocities and hence shallow ocean levels; (4) boundary scavenging can result in significant lateral redistribution of output fluxes for even very short residence time tracers (e.g., ²³⁰Th) if Péclet numbers are high; (5) the width of source and scavenging regions exerts a strong control over the actual tracer concentrations, but the spatial distribution and degree of tracer homogenization is not affected. The space dependence of input and scavenging is applicable to several reactive isotope tracers such as Be, Pb, Nd, Hf, Th, or Pa. Relative uniformity in their isotope ratios has been observed by mapping of these tracers in individual ocean basins [ von Blanckenburg and Igel, 1999 ]. Such uniformity would not be necessarily expected since the isotopes concerned enter through entirely different pathways. The simulations presented here demonstrate that homogenization of such short residence time tracers in ocean gyres is a feasible mechanism that can account for these observations.