Accelerating creep before catastrophic failure commonly follows a power‐law velocity‐acceleration relationship, with the exponent typically near 2 but often evolving from 1 to 2 at a certain point, indicating a dynamic transition. The underlying mechanisms, however, remain unclear. Here we investigate this transition by monitoring the slip displacement of clayey soil during fluid‐injection creep experiments. This transition is discontinuous in the first run but becomes continuous in the initially pre‐sheared sample. Using a regularized rate‐and‐state friction model, we explicitly examine the relationship between the exponent and the frictional properties of the soil. This model describes the dynamic transition, with the exponent evolving from 1 to 2 across a broad range of frictional parameters. Furthermore, by incorporating idealized shear localization processes, the model qualitatively reproduces the shear‐history‐dependent transition. Our study demonstrates that a combination of structural evolutions and frictional properties may explain slow and fast slips observed in various shear systems. Plain Language Summary: Predicting when materials will fail or natural hazards will occur is complex because it involves various physical processes and parameters. An empirical power‐law velocity‐acceleration relationship has proven effective and reliable for forecasting creep failure and natural events like landslides and volcanic eruptions. Although its exponent is typically 2, it can evolve from 1 to 2 over time, indicating a dynamic transition between two distinct acceleration regimes. In our fluid‐injection experiments on clayey soil, we observe a slow‐to‐fast transition in slip displacement and a multi‐layered shear zone. This transition is initially discontinuous but becomes continuous when the sample is pre‐sheared. To elucidate the mechanism, we use a slider block to simplify landslide movement, with the friction of the slip surface governed by a regularized rate‐and‐state friction model. For a velocity‐weakening slip surface, this model predicts a shift from velocity‐independent to velocity‐weakening steady‐state friction, demonstrating a continuous slow‐to‐fast transition with the exponent evolving from 1 to 2. Furthermore, the combination of friction and shear localization processes qualitatively reproduces the discontinuous transition observed in experiments. These results indicate that slow and fast slips can be modulated by both frictional property and structural evolution, encouraging the consideration of their combined effects. Key Points: Fluid‐injection creep experiments on clayey soil show two distinct acceleration regimes, with a dynamic transition based on shear historyThe regularized rate‐and‐state friction model describes the power‐law velocity‐acceleration relationships and exponents for both regimesThe model, coupled with idealized shear localization in a multilayer structure, qualitatively reproduces the history‐dependent transitions [ABSTRACT FROM AUTHOR]