Automated Machine Learning (AutoML) has been used successfully in settings where the learning task is assumed to be static. In many real-world scenarios, however, the data distribution will evolve over time, and it is yet to be shown whether AutoML techniques can effectively design online pipelines in dynamic environments. This study aims to automate pipeline design for online learning while continuously adapting to data drift. For this purpose, we design an adaptive Online Automated Machine Learning (OAML) system, searching the complete pipeline configuration space of online learners, including preprocessing algorithms and ensembling techniques. This system combines the inherent adaptation capabilities of online learners with the fast automated pipeline (re)optimization capabilities of AutoML. Focusing on optimization techniques that can adapt to evolving objectives, we evaluate asynchronous genetic programming and asynchronous successive halving to optimize these pipelines continually. We experiment on real and artificial data streams with varying types of concept drift to test the performance and adaptation capabilities of the proposed system. The results confirm the utility of OAML over popular online learning algorithms and underscore the benefits of continuous pipeline redesign in the presence of data drift.