Perceptual choices depend not only on the current sensory input, but also on the behavioral context. An important contextual factor is the history of one's own choices. Choice history often strongly biases perceptual decisions, and leaves traces in the activity of brain regions involved in decision processing. Yet, it remains unknown how such history signals shape the dynamics of later decision formation. Models of perceptual choice construe decision formation as the accumulation of sensory evidence towards decision bounds. In this framework, it is commonly assumed that choice history signals shift the starting point of accumulation towards the bound reflecting the previous choice. We here present results that challenge this idea. We fit a bounded accumulation ('drift diffusion') decision model to behavioral data from multiple perceptual choice tasks and sensory modalities, and estimated bias terms that dependent on observers' previous choices. Individual history biases in behavior were consistently explained by a history-dependent change in the evidence accumulation, rather than in its starting point. Choice history signals thus seem to affect the interpretation of current sensory input, akin to shifting endogenous attention towards (or away from) the previously selected interpretation.