Oceanic internal waves are a major driver for turbulent mixing in the ocean, which controls the global overturning circulation and the oceanic heat and carbon transport. Internal waves are observed to have a continuous energy distribution across all wave frequencies and scales, commonly known as the internal wave continuum, despite being forced at near-inertial and tidal frequencies at large scales. This internal wave continuum is widely thought to be developed primarily through wave-wave interactions. However, the development through wave-wave interactions occurs on yearly timescales and is insufficient to maintain the observed continuum given the large episodic wind energy input. Here we show, using realistic numerical simulations in the subpolar North Atlantic, that oceanic eddies rapidly distribute large-scale wind-forced near-inertial wave energy across spatio-temporal scales, thereby forming an internal wave continuum within three weeks. As a result, wave energy dissipation patterns are controlled by eddies and are significantly enhanced below the mixed layer. The efficiency of this process potentially explains why a phase lag between high-frequency and near-inertial wave energy was observed in eddy-poor regions but not in eddy-rich regions. Our findings highlight the importance of eddies in forming an internal wave continuum and in controlling upper ocean mixing patterns.