The application of machine learning algorithms as data-driven turbulence modelling tools for Reynolds Averaged Navier-Stokes (RANS) simulations is presented. A novel machine learning algorithm, called the Tensor Basis Random Forest (TBRF) is introduced, which is able to predict the Reynolds stress anisotropy tensor. The algorithm is trained on several flow cases using DNS/LES data, and used to predict the Reynolds stress anisotropy tensor on multiple test flow cases. Predictions are then propagated with a custom OpenFOAM solver to yield an improved flow field. Results show that the TBRF algorithm is able to accurately predict the anisotropy tensor for various flow cases, with most of the predictions being realizable and close to the DNS/LES reference data. Resulting mean flows for a square duct and a backward facing step show great resemblance to corresponding DNS and experimental data-sets.