Adjusting the stimulation parameters is a challenge in deep brain stimulation (DBS) therapy due to the vast number of different configurations available. As a result, systems based on the visualization of the volume of tissue activated (VTA) produced by a particular stimulation setting have been developed. However, the medical specialist still has to search, by trial and error, for a DBS set-up that generates the desired VTA. Therefore, our goal is developing a DBS parameter tuning strategy for current clinical devices that allows defining a target VTA under biophysically viable constraints. We propose a machine learning approach that allows estimating the DBS parameter values for a given VTA, which comprises two main stages: i) A K-nearest neighbors-based deformation to define a target VTA preserving biophysically viable constraints. ii) A parameter estimation stage that consists of a data projection using metric learning to highlight relevant VTA properties, and a regression/classification algorithm to estimate the DBS parameters that generate the target VTA. Our methodology allows setting a biophysically compliant target VTA and accurately predicts the required configuration of stimulation parameters. Also, the performance of our approach is stable for both isotropic and anisotropic tissue conductivities. Furthermore, the computational cost of the trained system is acceptable for real-world implementations.