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A thorough understanding of the heritability, genetic correlations and additive and non-additive variance components of tree growth and wood properties is a requisite for effective tree breeding. This knowledge is essential to maximize genetic gain, that is, the amount of increase in trait performance achieved annually through directional selection. Understanding the genetic attributes of traits targeted by breeding is also important to sustain decade-long genetic progress, that is, the progress made by increasing the average genetic value of the offspring as compared to that of the parental generation. In this study, we report quantitative genetic parameters for fifteen growth, wood chemical and physical traits for the world-famous Eucalyptus urograndis hybrid (E. grandis × E. urophylla). These traits directly impact the optimal use of wood for cellulose pulp, paper, and energy production. A population of 1,000 trees sampled in a progeny trial was phenotyped directly or following the development and use of near-infrared spectroscopy calibration models. Trees were genotyped with 33,398 SNPs and 24,001 DArT-seq genome-wide markers and genomic realized relationship matrices (GRM) were used for parameter estimation with an individual-tree additive-dominant mixed model. Wood chemical properties and wood density showed stronger genetic control than growth, cellulose and fiber traits. Additive effects are the main drivers of genetic variation for all traits, but dominance plays an equally or more important role for growth, singularly in this hybrid. GRM´s with >10,000 markers provided stable relationships estimates and more accurate parameters than pedigrees by capturing the full genetic relationships among individuals and disentangling the non-additive from the additive genetic component. Low correlations between growth and wood properties indicate that simultaneous selection for wood traits can be applied with minor effects on genetic gain for growth. Conversely, moderate to strong correlations between wood density and chemical traits exist, likely due to their interdependency on cell wall structure such that responses to selection will be connected for these traits. Our results illustrate the advantage of using genome-wide marker data to inform tree breeding in general and have important consequences for operational breeding of eucalypt urograndis hybrids., Competing Interests: The authors have declared that no competing interests exist. Author CG was employed by International Paper do Brasil. This commercial affiliation does not alter our adherence to all PLOS ONE policies on sharing data and materials.