Context: Model-Based Testing (MBT) was first introduced in 1970's, and has the potential to improve efficiency and effectiveness of testing. However, its adoption-especially for web applications-has been hindered by the effort required to manually design MBT models, and keep them updated. Objective: Based on the above challenge in a real industrial context, this study introduces an automated approach to reduce that effort by reverse engineering MBT models from clickstream data captured during users' interaction with web applications. Method: We have developed and present in this paper an open-source tool, named MBTModelGenerator, which logs user interactions via a lightweight JavaScript module in the front-end, and transmits them to a REST API backend. These interactions are then transformed into directly executable MBT models in the input format of an open-source MBT tool named GraphWalker. Results: The tool was evaluated on two representative open-source web applications, Spring PetClinic and a Task Manager web app, and is under evaluation in several large-scale industrial testing projects. The generated MBT models accurately reflected user navigation flows and could be executed in the GraphWalker MBT tool without any manual changes. Using the tool has significantly reduced the effort of MBT model design by more than 90%, while still allowing test engineers to inspect and refine the generated models for completeness. Conclusion: Our approach facilitates lightweight adoption of MBT by automating model generation, which is the most effort intensive phase of MBT. To ensure correctness and completeness, the generated models should still be reviewed by test engineers -- but that effort remains substantially lower than designing MBT models from scratch. The tool is in active industrial use and available as open-source for reuse and further development.