<p>The convergence of a stochastic optimal control problem with Markov switches in an averaging scheme is analyzed. A combination of the standard Wiener process and a uniformly ergodic Markov process is considered, allowing us to describe the system’s evolution under the influence of diffusion noise and random mode switches. The ergodic properties of the fast process and the conditions for the regularity of the coefficients are presented, which guarantee stable behavior of the system on average. The convergence in probability of the trajectories of the original system to the solutions of the marginal averaged system is proved (through <i>L</i>^<i>p</i>-estimates). The obtained results enable the solution of stochastic optimization and optimal control problems.</p>