Hydrodynamic transformations prescribe a redistribution of fluid trajectories and velocities within a localized transformation region while recovering an unmodified exterior flow. Realizing such transformations in a free-fluid Navier–Stokes system, however, requires closure of the associated momentum balance rather than a kinematic mapping alone. Existing transformation formulations are commonly derived from reduced momentum balances and do not generally retain the nonlinear convective transport of an ordinary Navier–Stokes flow. Here we formulate an inverse Navier–Stokes momentum-compensation operator that maps an admissible target velocity–pressure pair directly to the localized acceleration required to sustain its momentum balance. The operator retains both convective and viscous contributions and distinguishes kinematic admissibility from dynamic admissibility. For manufactured hydrodynamic concentrator and rotator transformations at Re _D = 100, the predicted compensation fields recover the prescribed velocity amplification and rotation with approximately second-order convergence. Applied to a no-slip cylinder wake, the same open-loop momentum compensation reduces the integrated streamwise surface-force coefficient from 1.37 to 0.0023 on the finest tested grid while redistributing wake momentum and vorticity according to global momentum balance diagnostics. Reynolds-number-dependent source norms reveal the continuous transition from viscous- to inertial-dominated compensation. The results establish the design of hydrodynamic transformations as an inverse Navier–Stokes momentum-closure problem and provide a general continuum framework for determining the localized momentum input required by prescribed flow transformations.