Electroencephalography (EEG) has wide-ranging applications, from clinical diagnosis to brain-computer interfaces (BCIs). With the increasing volume and variety of EEG data, there has been growing interest in establishing foundation models (FMs) to scale up and generalize neural decoding. Despite showing early potential, applying FMs to EEG remains challenging due to substantial inter-subject, inter-task, and inter-condition variability, as well as diverse electrode configurations across recording setups. To tackle these open challenges, we propose **NeurIPT**, a foundation model tailored for diverse EEG-based **Neur**al **I**nterfaces with a **P**re-trained **T**ransformer by capturing both homogeneous and heterogeneous spatio-temporal characteristics inherent in EEG signals. Temporally, we introduce Amplitude-Aware Masked Pretraining (AAMP), masking based on signal amplitude rather than random intervals, to learn robust representations across varying signal intensities beyond local interpolation. Moreover, this temporal representation is enhanced by a progressive Mixture-of-Experts (MoE) architecture, where specialized expert subnetworks are progressively introduced at deeper layers, adapting effectively to the diverse temporal characteristics of EEG signals. Spatially, NeurIPT leverages the 3D physical coordinates of electrodes, enabling effective transfer across varying EEG settings, and develops Intra-Inter Lobe Pooling (IILP) during fine-tuning to efficiently exploit regional brain features. Empirical evaluations across nine downstream BCI datasets, via fine-tuning and training from scratch, demonstrated NeurIPT consistently achieved state-of-the-art performance, highlighting its broad applicability and robust generalization. Our work pushes forward the state of FMs in EEG and offers insights into scalable and generalizable neural information processing systems.