Despite transformers' impressive accuracy, their computational cost is often prohibitive to use with limited computational resources. Most previous approaches to improve inference efficiency require a separate model for each possible computational budget. In this paper, we extend PoWER-BERT (Goyal et al., 2020) and propose Length-Adaptive Transformer that can be used for various inference scenarios after one-shot training. We train a transformer with LengthDrop, a structural variant of dropout, which stochastically determines a sequence length at each layer. We then conduct a multi-objective evolutionary search to find a length configuration that maximizes the accuracy and minimizes the efficiency metric under any given computational budget. Additionally, we significantly extend the applicability of PoWER-BERT beyond sequence-level classification into token-level classification with Drop-and-Restore process that drops word-vectors temporarily in intermediate layers and restores at the last layer if necessary. We empirically verify the utility of the proposed approach by demonstrating the superior accuracy-efficiency trade-off under various setups, including span-based question answering and text classification. Code is available at https://github.com/clovaai/length-adaptive-transformer.