Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper we derive explicit stabilized integrators of orders one and two for the optimal control of stiff systems. We analyze their favourable stability and symplecticity properties based on the continuous optimality conditions. Numerical experiments including the optimal control of a nonlinear diffusion-advection PDE illustrate the efficiency of the new approach.