In this paper we propose novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework. Within a hierarchical Bayesian formulation, the reconstructed image, the blur and the unknown hyperparameters for the image prior, the blur prior and the image degradation noise are simultaneously estimated. We develop two algorithms resulting from this formulation which provide approximations to the posterior distributions of the latent variables. Different values can be drawn from these distributions as estimates to the latent variables and the uncertainty of these estimates can be measured. Experimental results are provided to demonstrate the performance of the algorithms.