Predicting whether and how populations will adapt to rapid climate change is a critical goal for evolutionary biology. To examine the genetic basis of fitness and predict adaptive evolution in novel climates with seasonal variation, we grew a diverse panel of the annual plant Arabidopsis thaliana (multiparent advanced generation intercross lines) in controlled conditions simulating four climates: a present-day reference climate, an increased-temperature climate, a winter-warming only climate, and a poleward-migration climate with increased photoperiod amplitude. In each climate, four successive seasonal cohorts experienced dynamic daily temperature and photoperiod variation over a year. We measured 12 traits and developed a genomic prediction model for fitness evolution in each seasonal environment. This model was used to simulate evolutionary trajectories of the base population over 50 y in each climate, as well as 100-y scenarios of gradual climate change following adaptation to a reference climate. Patterns of plastic and evolutionary fitness response varied across seasons and climates. The increased-temperature climate promoted genetic divergence of subpopulations across seasons, whereas in the winter-warming and poleward-migration climates, seasonal genetic differentiation was reduced. In silico "resurrection experiments" showed limited evolutionary rescue compared with the plastic response of fitness to seasonal climate change. The genetic basis of adaptation and, consequently, the dynamics of evolutionary change differed qualitatively among scenarios. Populations with fewer founding genotypes and populations with genetic diversity reduced by prior selection adapted less well to novel conditions, demonstrating that adaptation to rapid climate change requires the maintenance of sufficient standing variation.