Twisted stacking of two-dimensional van der Waals (vdW) semiconductors creates moiré superlattices, which provides unprecedented control over quantum states and their light-matter interactions. We demonstrate that a simple twist interface between two single-crystalline bulks of hexagonal boron nitride (hBN) creates moiré quantum wells (QWs) embedded in a three-dimensional vdW structure. hBN moiré QWs strongly confine charge carriers under both optical excitation and electrical injection. Despite their indirect bandgap, they emit intense deep-ultraviolet luminescence in the extreme wavelength bands from 215 to 240 nanometers, exceeding that of state-of-the-art conventional aluminum gallium nitride (AlGaN) multiple QWs by more than an order of magnitude. Furthermore, the twist angle control allows wide tunability of luminescence energy and efficiency in moiré QWs.