In computational biology, predictive models are widely used to address complex tasks, but their performance can suffer greatly when applied to data from different distributions. The current state-of-the-art domain adaptation method for high-dimensional data aims to mitigate these issues by aligning the input dependencies between training and test data. However, this approach requires centralized access to both source and target domain data, raising concerns about data privacy, especially when the data comes from multiple sources. In this paper, we introduce a privacy-preserving federated framework for unsupervised domain adaptation in high-dimensional settings. Our method employs federated training of Gaussian processes and weighted elastic nets to effectively address the problem of distribution shift between domains, while utilizing secure aggregation and randomized encoding to protect the local data of participating data owners. We evaluate our framework on the task of age prediction using DNA methylation data from multiple tissues, demonstrating that our approach performs comparably to existing centralized methods while maintaining data privacy, even in distributed environments where data is spread across multiple institutions. Our framework is the first privacy-preserving solution for high-dimensional domain adaptation in federated environments, offering a promising tool for fields like computational biology and medicine, where protecting sensitive data is essential.