Objective We aim to bridge the gap between naturalistic studies of driver behavior and modern cognitive and neuroscientific accounts of decision making by modeling the cognitive processes underlying left-turn gap acceptance by human drivers. Background Understanding decisions of human drivers is essential for the development of safe and efficient transportation systems. Current models of decision making in drivers provide little insight into the underlying cognitive processes. On the other hand, laboratory studies of abstract, highly controlled tasks point towards noisy evidence accumulation as a key mechanism governing decision making. However, it is unclear whether the cognitive processes implicated in these tasks are as paramount to decisions that are ingrained in more complex behaviors, such as driving. Results The drivers’ probability of accepting the available gap increased with the size of the gap; importantly, response time increased with time gap but not distance gap. The generalized drift-diffusion model explained the observed decision outcomes and response time distributions, as well as substantial individual differences in those. Through cross-validation, we demonstrate that the model not only explains the data, but also generalizes to out-of-sample conditions. Conclusion Our results suggest that dynamic evidence accumulation is an essential mechanism underlying left-turn gap acceptance decisions in human drivers, and exemplify how simple cognitive process models can help to understand human behavior in complex real-world tasks. Application Potential applications of our results include real-time prediction of human behavior by automated vehicles and simulating realistic human-like behaviors in virtual environments for automated vehicles.