Learning in non-stationary environments is one of the biggest challenges in machine learning. Non-stationarity can be caused by either task drift, i.e., the drift in the conditional distribution of labels given the input data, or the domain drift, i.e., the drift in the marginal distribution of the input data. This paper aims to tackle this challenge in the context of continuous domain adaptation, where the model is required to learn new tasks adapted to new domains in a non-stationary environment while maintaining previously learned knowledge. To deal with both drifts, we propose variational domain-agnostic feature replay, an approach that is composed of three components: an inference module that filters the input data into domain-agnostic representations, a generative module that facilitates knowledge transfer, and a solver module that applies the filtered and transferable knowledge to solve the queries. We address the two fundamental scenarios in continuous domain adaptation, demonstrating the effectiveness of our proposed approach for practical usage.