Genomic offset statistics predict the maladaptation of populations to rapid habitat alteration based on association of genotypes with environmental variation. Despite substantial evidence for empirical validity, genomic offset statistics have well identified limitations, and lack a theory that would facilitate interpretations of predicted values. Here, we clarified the theoretical relationships between genomic offset statistics and adaptive traits, and proposed a geometric measure to predict fitness after rapid change in local environment. The predictions of our theory were verified in computer simulations and in empirical data on African pearl millet ( Cenchrus americanus ) obtained from a common garden experiment. Our results proposed a unified perspective on genomic offset statistics, and provided a theoretical foundation necessary when considering their potential application in conservation management in the face of environmental change. Significance statement Maladaptation to altered habitat resulting from environmental change causes shifts in adaptive traits of natural populations. Adaptive shifts are best evaluated from experiments in which organisms are placed into an environment that differs from the one in which the traits evolved, but those experiments are costly and time consuming. Genomic offsets predict shifts from environmental and genomic data without trait observations. We developed a novel theory for genomic offset statistics to predict fitness in altered conditions. Our theory introduces a geometric measure, and unifies previously proposed genomic offset statistics in a common framework. Validation from simulated and empirical data provides support for the theory, and paves the way for further advances in predictive ecological genomics.