Niche dimensionality is suggested to be a key determinant of ecological speciation ("multifarious selection" hypothesis), but genetic aspects of this process have not been investigated theoretically. We use Fisher's geometrical model to study how niche dimensionality influences the mean fitness of hybrids formed upon secondary contact between populations adapting in allopatry. Gaussian selection for an optimum generates two forms of reproductive isolation (RI): an extrinsic component due to maladaptation of the mean phenotype, and an intrinsic variance load resulting from what we term transgressive incompatibilities between mutations fixed in different populations. We show that after adaptation to a new environment, RI increases with (1) the mean initial maladaptation of diverging population, and (2) niche dimensionality, which increases the phenotypic variability of fixed mutations. Under mutation selection drift equilibrium in a constant environment, RI accumulates steadily with time, at a rate that also increases with niche dimensionality. A similar pattern can be produced by successive shifts in the optimum phenotype. Niche dimensionality thus has an effect per se on postzygotic isolation, beyond putative indirect effects (stronger selection, more genes). Our mechanism is consistent with empirical evidence about transgressive segregation in crosses between divergent populations, and with patterns of accumulation of RI with time in many taxa.