Bacterial biofilms represent a major form of microbial life on Earth and serve as a model active nematic system, in which activity results from growth of the rod-shaped bacterial cells. In their natural environments, ranging from human organs to industrial pipelines, biofilms have evolved to grow robustly under significant fluid shear. Despite intense practical and theoretical interest, it is unclear how strong fluid flow alters the local and global architectures of biofilms. Here, we combine highly time-resolved single-cell live imaging with 3D multiscale modeling to investigate the mechanisms by which flow affects the dynamics of all individual cells in growing biofilms. Our experiments and cell-based simulations reveal three quantitatively different growth phases in strong external flow and the transitions between them. In the initial stages of biofilm development, flow induces a downstream gradient in cell orientation, causing asymmetrical dropletlike biofilm shapes. In the later developmental stages, when the majority of cells are sheltered from the flow by the surrounding extracellular matrix, buckling-induced cell verticalization in the biofilm core restores radially symmetric biofilm growth, in agreement with predictions of a 3D continuum model.