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The interface control domain decomposition (ICDD) method of Discacciati, Gervasio, and Quarteroni [SIAM J. Control Optim., 51 (2013), pp. 3434--3458, doi:10.1137/120890764; J. Coupled Syst. Multiscale Dyn., 1 (2013), pp. 372--392, doi:10.1166/jcsmd.2013.1026] is proposed here to solve the coupling between Stokes and Darcy equations. According to this approach, the problem is formulated as an optimal control problem whose control variables are the traces of the velocity and the pressure on the internal boundaries of the subdomains that provide an overlapping decomposition of the original computational domain. A theoretical analysis is carried out, and the well-posedness of the problem is proved under certain assumptions on both the geometry and the model parameters. An efficient solution algorithm is proposed, and several numerical tests are implemented. Our results show the accuracy of the ICDD …