The invention describes an adapter part (2, 9) for a modular lighting assembly (1) comprising a number of light-emitting diodes (4) mounted on a separate base part (3), which adapter part (2, 9) comprises a number of first electrical connectors (21) arranged to connect the light-emitting diodes (4) to an external power supply; at least one electrical component (5) arranged in a body of the adapter part (2, 9); and a number of second electrical connectors (22) arranged to connect external circuitry to an electrical component (5) arranged in the body of the adapter part (2, 9). The invention further describes a modular lighting assembly (1) comprising a base part (3) upon which a number of light-emitting diodes (4) is mounted; and an adapter part (2, 9) according to the invention. The invention also describes a method of assembling such a modular lighting arrangement (1), comprising the steps of connecting a first adapter part (2, 9) according to the invention to a separate base part (3); choosing a number of electrical components (5, 6) on the basis of an application requirement of the modular lighting arrangement (1); and arranging an electrical component (5, 6) in the adapter part (2, 9) such that an electrical connection is formed between a contact surface of the electrical component (5, 6) and a second electrical connector (22) of the adapter part (2, 9).