Since the onset of the pandemic, many SARS-CoV-2 variants have emerged, exhibiting substantial evolution in the virus spike protein, the main target of neutralizing antibodies. A plausible hypothesis proposes that the virus evolves to evade antibody-mediated neutralization (vaccine- or infection-induced) to maximize its ability to infect an immunologically experienced population. While virus infection induces neutralizing antibodies, viral evolution may thus navigate on a dynamic immune landscape that resulted from the infection history in different regions. Global inequalities in vaccine distribution and differences in infection-prevention measures have shaped this global immunological landscape, resulting in uneven geographic distributions of SARS-CoV-2 variants. Consequently, predicting which variant will spread within particular regions has become increasingly challenging. To tackle this challenge, we developed a comprehensive mechanistic model of the dynamic immunological landscape of SARS-CoV-2. We utilized deep-mutational scanning data and antibody pharmacokinetics to compute time-dependent cross-neutralization between arbitrary variants. Combined with infection history and molecular surveillance data, we could predict the variant-specific relative number of susceptibles over time, exemplified for Germany. This quantity precisely matched historical variant dynamics, predicted future variant dynamics, and could explain global differences in variant dynamics. Our work strongly supports the hypothesis that SARS-CoV-2 evolution is driven by escape from humoral immunity, allows contextualizing risk assessment of variants, and provides important clues for vaccine design.