Coherent gigahertz-frequency surface acoustic waves (SAWs) traveling on the surface of a piezoelectric crystal can, via the magnetoelastic interaction, resonantly excite traveling surface spin waves in an adjacent thin-film ferromagnet. These excited surface spin waves, traveling with a definite in-plane wave-vector q∥ enforced by the SAW, can be detected by measuring changes in the electro-acoustical transmission of a SAW delay line. Here, we provide a demonstration that such measurements constitute a precise and quantitative technique for spin-wave spectroscopy, providing a means to determine both isotropic and anisotropic contributions to the spin-wave dispersion and damping. We demonstrate the effectiveness of this spectroscopic technique by measuring the spin-wave properties of a Ni thin film for a large range of wave vectors, | q ∥ | = 2.5 × 104-8 × 104cm-1, over which anisotropic dipolar interactions vary from being negligible to quite significant. © 2015 AIP Publishing LLC.