Multi-task dense prediction, which aims to jointly solve tasks like semantic segmentation and depth estimation, is crucial for robotics applications but suffers from domain shift when deploying models in new environments. While unsupervised domain adaptation (UDA) addresses this challenge for single tasks, existing multi-task UDA methods primarily rely on adversarial learning approaches that are less effective than recent self-training techniques. In this paper, we introduce FAMDA, a simple yet effective UDA framework that addresses this limitation by leveraging Vision Foundation Models (VFMs) as powerful teachers within a self-training paradigm. Our approach integrates Segmentation and Depth foundation models into a self-training paradigm to generate high-quality pseudo-labels for the target domain, effectively distilling their robust generalization capabilities into a single, efficient student network. Extensive experiments show that FAMDA achieves state-of-the-art (SOTA) performance on standard synthetic-to-real UDA multi-task learning (MTL) benchmarks and a challenging new day-to-night adaptation task. Our framework enables the training of highly efficient models; a lightweight variant achieves SOTA accuracy while being more than 10X smaller than foundation models, highlighting FAMDA's suitability for creating domain-adaptive and efficient models for resource-constrained robotics applications.