The dinoflagellate-coral partnership influences host tolerance to thermal stress that causes bleaching. However, the comparative roles of host genetic versus environmental factors in determining the composition of this symbiosis are largely unknown. Here we quantify the heritability of Symbiodinium communities in two broadcast spawning corals with different symbiont transmission modes: Acropora tenuis has environmental acquisition, and Montipora digitata has maternal transmission. Using high throughput sequencing of the ITS-2 region to characterize communities in parental colonies, juveniles and eggs, we describe new Symbiodinium types in both coral species and previously unknown symbiont dynamics. After one month of natural uptake in the field, Symbiodinium communities associated with A. tenuis juveniles were dominated by A3, C1, D1, A-type CCMP828, and D1a in proportional abundances that were conserved across two years. In contrast, M. digitata eggs were characterized by C15, D1, and A3. On average, host genetic influences accounted for 29% of phenotypic variation found in Symbiodinium communities in A. tenuis and 62% in M. digitata. Our results reveal hitherto unknown flexibility in the acquisition of Symbiodinium communities and substantial heritability in both species provides ample material for selection to produce partnerships that are locally adapted to changing environmental conditions.