We present the first lattice QCD determination of the Ξ b → Ξ vector, axial-vector, and tensor form factors, which are relevant for the theory of rare decays including Ξ b → Ξ ℓ + ℓ − and Ξ b → Ξ γ . The calculation is performed with 2 + 1 flavors of domain-wall fermions at three different lattice spacings and pion masses in the range from approximately 430 to 230 MeV. The bottom quark is implemented using an anisotropic clover action. Three-point functions with a wide range of source-sink separations and model averaging are used to extract the ground-state contributions. We fit the dependence of the form factors on the momentum transfer, the pion mass, and the lattice spacing using modified z expansions that account for subthreshold branch cuts, and apply dispersive bounds and asymptotic behavior constraints to achieve controlled uncertainties in the full semileptonic kinematic region. Using our form factor results, we present standard model predictions for the Ξ b − → Ξ − γ and Ξ b − → Ξ − μ + μ − branching fractions and two angular observables.