Electronic devices may include displays. A display may include a display unit that includes an array of display pixels and a backlight unit that provides backlight illumination for the display pixels. An automated alignment system may be used to align the display unit to the backlight unit. The alignment system may include a camera, a control unit, and computer-controlled positioners. The control unit may gather alignment feature location information from the display unit and the backlight unit using the camera. The control unit may determine a centroid of the backlight unit based on the alignment feature location information. The alignment feature location information may include the respective locations of openings in the backlight unit. The control unit may operate computer-controlled positioners to align the display unit with respect to the backlight unit using the centroid and to subsequently attach the display unit to the backlight unit.