Fiber tractography based on Diffusion MRI measurements is a valuable tool for the detection and visual representation of neural pathways in vivo. We present a novel fiber orientation distribution function (ODF) based streamline tractography approach which incorporates information of neighboring regions derived from a Bayesian model. In each iteration step, the proposed algorithm defines a set of candidate fiber fragments continuing the already tracked path and assigns an a-posteriori probability. We compute the posterior as the normalized product of a likelihood function based on the given ODF-field and a prior distribution representing anatomical plausibility of a candidate fiber fragment with respect to tract curvature derived from the previously tracked fiber path by an extrapolation strategy. We derive both a deterministic tractography algorithm obtaining in each iteration a tracking direction by maximum a-posteriori estimation, as well as a probabilistic version drawing a direction from the marginalized posterior distribution. Compared to fiber tracking methods that rely only on the local ODF, the proposed algorithm proves more robust in the presence of noise and partial volume effects. We demonstrate the effectiveness of both our deterministic and probabilistic method on simulated, phantom, and in vivo data.