This paper proposes a novel data-driven approach for feedback linearization of nonlinear control-affine systems by leveraging the Koopman operator framework. We establish theoretical connections between feedback linearization on the original state manifold and the higher-dimensional Koopman observable manifold using concepts from system immersion. For systems with exact Koopman bilinear representations, we provide closed-form solutions to the feedback linearization problem without solving partial differential equations. When exact bilinear representations are not available, we develop an approximate method based on singular value decomposition that converges to the exact solution as the observables are enriched. The simulation results and numerical examples demonstrate the effectiveness of the approach.