Regularized diffusion tensor estimation is an essential step in DTI analysis. There are many methods proposed in literature for this task but most of them are neither statistically robust nor feature preserving denoising techniques that can simultaneously estimate symmetric positive definite (SPD) diffusion tensors from diffusion MRI. One of the most popular techniques in recent times for feature preserving scalar- valued image denoising is the non-local means filtering method that has recently been generalized to the case of diffusion MRI denoising. However, these techniques denoise the multi-gradient volumes first and then estimate the tensors rather than achieving it simultaneously in a unified approach. Moreover, some of them do not guarantee the positive definiteness of the estimated diffusion tensors. In this work, we propose a novel and robust variational framework for the simultaneous smoothing and estimation of diffusion tensors from diffusion MRI. Our variational principle makes use of a recently introduced total Kullback-Leibler (tKL) divergence, which is a statistically robust similarity measure between diffusion tensors, weighted by a non-local factor adapted from the traditional non-local means filters. For the data fidelity, we use the nonlinear least-squares term derived from the Stejskal-Tanner model. We present experimental results depicting the positive performance of our method in comparison to competing methods on synthetic and real data examples.