Traditional knowledge distillation (KD) methods manually design student architectures to compress large models given pre-specified computational cost. This requires several trials to find viable students, and repeating the process with change in computational budget. We use Neural Architecture Search (NAS) to automatically distill several compressed students with variable cost from a large model. Existing NAS methods train a single SuperLM consisting of millions of subnetworks with weight-sharing, resulting in interference between subnetworks of different sizes. Additionally, many of these works are task-specific requiring task labels for SuperLM training. Our framework AutoDistil addresses above challenges with the following steps: (a) Incorporates inductive bias and heuristics to partition Transformer search space into K compact sub-spaces (e.g., K=3 can generate typical student sizes of base, small and tiny); (b) Trains one SuperLM for each sub-space using task-agnostic objective (e.g., self-attention distillation) with weight-sharing of students; (c) Lightweight search for the optimal student without re-training. Task-agnostic training and search allow students to be reused for fine-tuning on any downstream task. Experiments on GLUE benchmark demonstrate AutoDistil to outperform state-of-the-art KD and NAS methods with upto 3x reduction in computational cost and negligible loss in task performance. Code and model checkpoints are available at https://github.com/microsoft/autodistil.