The invention relates to a LED vehicle headlight. Each light unit has a LED board with a luminous surface and an optical device associated with a reflector and/or a lens. A reflector holder carries the optical devices of the light units and is formed in one piece with the latter. A board holder is fastened detachably to the reflector holder. The board holder has a receptacle for each light unit, and the LED board has contact surfaces that come into contact with corresponding contact surfaces on the reflector holder to position the LED board with respect to the assigned optical device when the board holder is fixed on the reflector holder. Each light unit has elastic pressurizing means that act on the LED board in order to press its contact surfaces against the contact surfaces of the reflector holder when the board holder is fixed on the reflector holder.