A system of interlocking LED panel tiles includes a first tile having at least one layer of light emitting diodes (LEDs) provided on a substrate, where the substrate is mounted on a substantially rectangular supporting plate having interlocking features. The substrate overlaps the interlocking features. The first tile has a set of positive and negative voltage conductors running between the two sets of opposite edges of the tile as busses. Multiple identical tiles are provided. Each tile has the interlocking features along their edges that firmly physically connect to abutting tiles to create a lamp having any pattern of tiles selected by the user. By interlocking the tiles, the positive and negative conductors are automatically connected to electrically connect the LEDs in the tiles in parallel, and the interlocking features are hidden by the overlying substrate. Additional conductors may be used to provide greater interconnection flexibility.