Robots are traditionally bound by a fixed morphology during their operational lifetime, which is limited to adapting only their control strategies. Here we present the first quadrupedal robot that can morphologically adapt to different environmental conditions in outdoor, unstructured environments. Our solution is rooted in embodied AI and comprises two components: (1) a robot that permits in situ morphological adaptation and (2) an adaptation algorithm that transitions between the most energy-efficient morphologies on the basis of the currently sensed terrain. We first build a model that describes how the robot morphology affects performance on selected terrains. We then test continuous adaptation on realistic outdoor terrain while allowing the robot to constantly update its model. We show that the robot exploits its training to effectively transition between different morphological configurations, exhibiting substantial performance improvements over a non-adaptive approach. The demonstrated benefits of real-world morphological adaptation demonstrate the potential for a new embodied way of incorporating adaptation into future robotic designs.