We propose an efficient and provably correct active-set based algorithm for solving the elastic net problem. The proposed algorithm exploits the fact that the nonzero entries of the elastic-net solution fall into an oracle region, which we use to define and efficiently update our active-set estimate. The proposed update rule leads to an iterative algorithm that is shown to converge to the optimal solution in a finite number of iterations. We present experiments for subspace clustering on computer vision datasets that demonstrate the superiority of our method in terms of clustering accuracy and scalability.