Grafting is typically utilized to merge adapted seedling rootstocks with highly productive clonal scions. This process implies the interaction of multiple genomes to produce a unique tree phenotype. However, the interconnection of both genotypes obscures individual contributions to phenotypic variation (rootstock-mediated heritability), hampering tree breeding. Therefore, our goal was to quantify the inheritance of seedling rootstock effects on scion traits using avocado (Persea americana Mill.) cv. Hass as a model fruit tree. We characterized 240 diverse rootstocks from 8 avocado cv. Hass orchards with similar management in three regions of the province of Antioquia, northwest Andes of Colombia, using 13 microsatellite markers simple sequence repeats (SSRs). Parallel to this, we recorded 20 phenotypic traits (including morphological, biomass/reproductive, and fruit yield and quality traits) in the scions for 3 years (2015–2017). Relatedness among rootstocks was inferred through the genetic markers and inputted in a “genetic prediction” model to calculate narrow-sense heritabilities (h2) on scion traits. We used three different randomization tests to highlight traits with consistently significant heritability estimates. This strategy allowed us to capture five traits with significant heritability values that ranged from 0.33 to 0.45 and model fits (r) that oscillated between 0.58 and 0.73 across orchards. The results showed significance in the rootstock effects for four complex harvest and quality traits (i.e., total number of fruits, number of fruits with exportation quality, and number of fruits discarded because of low weight or thrips damage), whereas the only morphological trait that had a significant heritability value was overall trunk height (an emergent property of the rootstock–scion interaction). These findings suggest the inheritance of rootstock effects, beyond root phenotype, on a surprisingly wide spectrum of scion traits in “Hass” avocado. They also reinforce the utility of polymorphic SSRs for relatedness reconstruction and genetic prediction of complex traits. This research is, up to date, the most cohesive evidence of narrow-sense inheritance of rootstock effects in a tropical fruit tree crop. Ultimately, our work highlights the importance of considering the rootstock–scion interaction to broaden the genetic basis of fruit tree breeding programs while enhancing our understanding of the consequences of grafting.