Transformer-based language models such as BERT provide significant accuracy improvement to a multitude of natural language processing (NLP) tasks. However, their hefty computational and memory demands make them challenging to deploy to resource-constrained edge platforms with strict latency requirements. We present EdgeBERT an in-depth and principled algorithm and hardware design methodology to achieve minimal latency and energy consumption on multi-task NLP inference. Compared to the ALBERT baseline, we achieve up to 2.4x and 13.4x inference latency and memory savings, respectively, with less than 1%-pt drop in accuracy on several GLUE benchmarks by employing a calibrated combination of 1) entropy-based early stopping, 2) adaptive attention span, 3) movement and magnitude pruning, and 4) floating-point quantization. Furthermore, in order to maximize the benefits of these algorithms in always-on and intermediate edge computing settings, we specialize a scalable hardware architecture wherein floating-point bit encodings of the shareable multi-task embedding parameters are stored in high-density non-volatile memory. Altogether, EdgeBERT enables fully on-chip inference acceleration of NLP workloads with 5.2x, and 157x lower energy than that of an un-optimized accelerator and CUDA adaptations on an Nvidia Jetson Tegra X2 mobile GPU, respectively.