  We compute the ${\cal O}(\alpha^2\alpha_s^2)$ perturbative corrections to
inclusive jet production in electron-nucleon collisions. This process is of
particular interest to the physics program of a future Electron Ion Collider
(EIC). We include all relevant partonic processes, including deep-inelastic
scattering contributions, photon-initiated corrections, and parton-parton
scattering terms that first appear at this order. Upon integration over the
final-state hadronic phase space we validate our results for the deep-inelastic
corrections against the known next-to-next-to-leading order (NNLO) structure
functions. Our calculation uses the $N$-jettiness subtraction scheme for
performing higher-order computations, and allows for a completely differential
description of the deep-inelastic scattering process. We describe the
application of this method to inclusive jet production in detail, and present
phenomenological results for the proposed EIC. The NNLO corrections have a
non-trivial dependence on the jet kinematics and arise from an intricate
interplay between all contributing partonic channels.
