Equipped with easy-to-access micro computation access points, the fog computing architecture provides low-latency and ubiquitously available computation offloading services to many simple and cheap Internet of Things devices with limited computing and energy resources. One obstacle, however, is how to seamlessly hand over mobile IoT devices among different computation access points when computation offloading is in action so that the offloading service is not interrupted -- especially for time-sensitive applications. In this article, we propose Follow Me Fog (FMF), a framework supporting a new seamless handover timing scheme among different computation access points. Intrinsically, FMF supports a job pre-migration mechanism, which pre-migrates computation jobs when the handover is expected to happen. Such expectations can be indicated by constantly monitoring received signal strengths. Then we present the design and a prototype implementation of FMF. Our evaluation results demonstrate that FMF can achieve a substantial latency reduction (36.5 percent in our experiment). In conclusion, the FMF design clears a core obstacle, allowing fog computing to provide interruption-resistant services to mobile IoT devices.