The label shift hypothesis posits that the source and target domains exhibit differing label priors while maintaining identical conditional probabilities. This core assumption enables models to adapt to domain distribution discrepancies through loss re-weighting or classifier output calibration, making it a prominent focus in open-environment machine learning. However, the prevalent existence of label noise severely degrades the classification efficacy of source classifiers, fundamentally undermining traditional label shift adaptation approaches. To address the dual challenges of label shift and label noise, we propose the Denoising Expectation-Maximization (DNEM) framework, which enhances model robustness against distribution shifts and label noise via iterative estimation of noise transition matrices and optimization of importance weights. Leveraging the memorization effect in deep learning, DNEM dynamically adjusts the learning rate for noise matrix estimation, maintaining conservative updates during initial training phases to preserve knowledge from relatively clean labels. Extensive experiments on multiple benchmark datasets demonstrate that DNEM consistently outperforms state-of-the-art methods under high noise rates and diverse shift conditions.