The problem of output regulation for linear stochastic systems is addressed. Wefirst define and solve the ideal problem of output regulation via error feedback. We note thatits solution is not implementable in practice because the Brownian motion is not available formeasure. Therefore, we define an approximate problem for which we provide a practical solution.The implemented controller is hybrid, in that a continuous-time, deterministic control law issupplemented by a discrete-time, stochastic correction. This correction is performed using ana-posterioriapproximation of the variations of the Brownian motion provided by a nonlinearestimator. The resulting hybrid closed-loop system is nonlinear, as the scalars approximatingthe increments of the Brownian motion depend nonlinearly on the states and the inputs. Theerror between the solution of the approximate problem and the solution of the ideal problem ischaracterised. We show that the ideal solution is retrieved as the sampling time tends to zero.We illustrate the results by means of a numerical example.