A series of complexes [Cu2X2(Pic3PO)2] (X = Cl, Br, I) based on tris(pyridin-2-ylmethyl)phosphine oxide (Pic3PO) has been synthesized. At 298 K, these compounds exhibit thermally activated delayed fluorescence (TADF) of 1(M+X)LCT type with λmax varying from 485 to 545 nm, and quantum efficiency up to 54%. In the TADF process, the halide effect appears as the emission intensification and bathochromic shift of λmax in the following order X = I < Br < Cl. Upon X-ray irradiation, the title compounds emit radioluminescence, the emission bands of which have the same shape as those at TADF, thereby meaning a similar radiative excited state. By contrast to TADF, the halide effect in the radioluminescence is reversed: its intensity grows in the order X = Cl < Br < I, since heavier atoms absorb X-rays more efficiently. These findings essentially contribute to our knowledge about the halide effect in the photo- and radioluminescent Cu(I) halide emitters.