We present discrete-time approximation of optimal control policies for infinite horizon discounted/ergodic control problems for controlled diffusions in $\Rd$\,. In particular, our objective is to show near optimality of optimal policies designed from the approximating discrete-time controlled Markov chain model, for the discounted/ergodic optimal control problems, in the true controlled diffusion model (as the sampling period approaches zero). To this end, we first construct suitable discrete-time controlled Mark…