Mature B-cell exit from germinal centers is controlled by a transcriptional regulatory module that integrates antigen and T-cell signals and, ultimately, leads to terminal differentiation into memory B cells or plasma cells. Despite a compact structure, the module dynamics are highly complex because of the presence of several feedback loops and self-regulatory interactions, and understanding its dysregulation, frequently associated with lymphomagenesis, requires robust dynamical modeling techniques. We present a quantitative kinetic model of three key gene regulators, BCL6, IRF4, and BLIMP, and use gene expression profile data from mature human B cells to determine appropriate model parameters. The model predicts the existence of two different hysteresis cycles that direct B cells through an irreversible transition toward a differentiated cellular state. By synthetically perturbing the interactions in this network, we can elucidate known mechanisms of lymphomagenesis and suggest candidate tumorigenic alterations, indicating that the model is a valuable quantitative tool to simulate B-cell exit from the germinal center under a variety of physiological and pathological conditions.