Foundation models for EEG analysis are still in their infancy, limited by two key challenges: (1) variability across datasets caused by differences in recording devices and configurations, and (2) the low signal-to-noise ratio (SNR) of EEG, where brain signals are often buried under artifacts and non-brain sources. To address these challenges, we present EEG-X, a device-agnostic and noise-robust foundation model for EEG representation learning. EEG-X introduces a novel location-based channel embedding that encodes spatial information and improves generalization across domains and tasks by allowing the model to handle varying channel numbers, combinations, and recording lengths. To enhance robustness against noise, EEG-X employs a noise-aware masking and reconstruction strategy in both raw and latent spaces. Unlike previous models that mask and reconstruct raw noisy EEG signals, EEG-X is trained to reconstruct denoised signals obtained through an artifact removal process, ensuring that the learned representations focus on neural activity rather than noise. To further enhance reconstruction-based pretraining, EEG-X introduces a dictionary-inspired convolutional transformation (DiCT) layer that projects signals into a structured feature space before computing reconstruction (MSE) loss, reducing noise sensitivity and capturing frequency- and shape-aware similarities. Experiments on datasets collected from diverse devices show that EEG-X outperforms state-of-the-art methods across multiple downstream EEG tasks and excels in cross-domain settings where pre-trained and downstream datasets differ in electrode layouts. The models and code are available at: https://github.com/Emotiv/EEG-X