Micro-LEDs (µLEDs) have been explored for augmented and virtual reality display applications that require extremely high pixels per inch and luminance. However, conventional manufacturing processes based on the lateral assembly of red, green and blue (RGB) µLEDs have limitations in enhancing pixel density. Recent demonstrations of vertical µLED displays have attempted to address this issue by stacking freestanding RGB LED membranes and fabricating top-down, but minimization of the lateral dimensions of stacked µLEDs has been difficult. Here we report full-colour, vertically stacked µLEDs that achieve, to our knowledge, the highest array density (5,100 pixels per inch) and the smallest size (4 µm) reported to date. This is enabled by a two-dimensional materials-based layer transfer technique15,16,17,18 that allows the growth of RGB LEDs of near-submicron thickness on two-dimensional material-coated substrates via remote or van der Waals epitaxy, mechanical release and stacking of LEDs, followed by top-down fabrication. The smallest-ever stack height of around 9 µm is the key enabler for record high µLED array density. We also demonstrate vertical integration of blue µLEDs with silicon membrane transistors for active matrix operation. These results establish routes to creating full-colour µLED displays for augmented and virtual reality, while also offering a generalizable platform for broader classes of three-dimensional integrated devices.