A three-orbital-model approach for studying spin-wave excitations in the strongly spin-orbit coupled layered perovskite iridates is presented which provides a unified description of magnetic excitations as well as the electronic band structure. The calculated spin-wave dispersions with realistic three-band parameters are in excellent agreement with the resonant inelastic x-ray scattering (RIXS) data for iridates, including the strong antiferromagnet zone-boundary dispersion in the single-layer compound Sr2IrO4 and the large anisotropy gap in the bilayer compound Sr3Ir2O7. The RIXS spin-wave data are shown to provide evidence of mixing between the J=12 and 32 sectors in both compounds.