Robot imitation learning is limited by the scarcity of action-labeled data, while action-free demonstrations such as videos are abundant. Recent latent-action methods learn action-relevant representations from observation transitions, but they do not optimize latent actions for downstream control, leading to latent representations that are difficult for policies to model and difficult to accurately decode into continuous robot actions. This paper introduces ELA, an end-to-end framework for learning from video demonstrations via latent actions jointly optimized for policy learning and action decoding. ELA jointly trains a latent action model, latent action policy, and action decoder, enabling policies to leverage abundant video data with only a handful of action-labeled robot demonstrations. Experiments on simulated and real-world manipulation tasks show that ELA consistently outperforms prior latent action baselines. Moreover, it integrates seamlessly with existing imitation learning methods through lightweight 4M-parameter action decoders, requiring no changes to policy architectures or training objectives. Additional materials can be found on: https://end2end-latent-action.github.io/