The nonlinear evolution of two-dimensional instability waves in a fully submerged wake is studied numerically through direct numerical simulation of the incompressible Euler equations subject to the dynamic and kinematic boundary conditions on the ocean surface. For a parallel, fully submerged wake flow, the sinuous mode of linear instability is more unstable than the varicose mode. Therefore, the nonlinear evolution of the instability results in a staggered-vortex pattern in ;the bulk of the fluid, while the free-surface signature depends on the submergence depth of the mean velocity profile and ~the Froude number of the flow. Specifically, for large submergence depth and low Froude number, the flow reaches a quasi-equilibrium state, where the free surface takes the form of a propagating gravity wave with a very small height. However, for the same submergence depth, increasing the Froude number beyond a certain value causes breaking of the free-surface wave. For high Froude number, wave breaking is caused by the presence of a sharp vertical velocity shear along the free surface for deep and shallow wakes alike. For small submergence depth, on the other hand, the free-surface wave breaks even for low Froude number, because of the sharp horizontal velocity shear that is induced along the free surface by the vortices of the flow.