Systematic neutron-scattering experiments have been carried out in order to reveal the crystal and magnetic structures as well as the magnetic excitation in the Ce-based intermetallic compound ${\mathrm{CeAgSb}}_{2}.$ It was clarified that the Ag atoms in ${\mathrm{CeAgSb}}_{2}$ (space group: $\mathrm{P}4/nmm)$ occupy the 2b site, while Sb atoms occupy $2a$ and $2c$ sites, which have, to date, been controversial in literature. From the analysis of neutron powder-diffraction profile, we found the existence of the ferromagnetic component of about $0.41{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Ce}$ oriented along the c axis, consistent with the result of previous studies. On the other hand, however, no trace of the antiferromagnetic or spin-density wave peak was detected within our range of experimental accuracy. We observed a considerable spin-wave excitation below 3 meV. The dispersion relation was explained by the anisotropic Heisenberg model. This means that ${\mathrm{CeAgSb}}_{2}$ has a simple ferromagnetic structure. Furthermore, crystalline electric-field (CEF) excitations were observed at 5.2 and 12.5 meV in the paramagnetic state, which is indicative of the localized nature of the $\mathrm{Ce}\ensuremath{-}4f$ electron. Our analysis revealed that $|{J}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}〉$ is the ground state, while the first and second excited levels are mainly due to $|\ifmmode\pm\else\textpm\fi{}\frac{3}{2}〉$ and $|\ifmmode\pm\else\textpm\fi{}\frac{5}{2}〉,$ respectively. The observed ferromagnetic moment is in good agreement with the ground-state saturation moment, ${g}_{J}{\ensuremath{\mu}}_{\mathrm{B}}{J}_{\mathrm{z}}\ensuremath{\sim}0.43{\ensuremath{\mu}}_{\mathrm{B}}.$ The susceptibility, magnetization curve, and magnetostriction can be explained in terms of the CEF level scheme with anisotropic exchange interaction.