Antennas with a massive amount of elements at one end are among 5G mobile communication key technologies for which spectral efficiency is enhanced by serving many users in parallel over tailored minimally interfering beams. This requires channel models that characterize the propagation environment in both azimuth and elevation. Additionally, the channel model has to capture spatial correlation effects among closely located positions, knowing that the propagation characteristics change gradually over the network area. In order to simulate mobile users or advanced beamforming strategies based on user location or angular information, it is crucial that spatial consistency is included in the applied channel models. This paper introduces a novel model for spatial consistency that is applicable to all prevalent geometry-based stochastic channel models. We provide a detailed explanation of the model and analyze its statistical properties and show its behavior when applied to the 3GPP 3D channel model as an example. To validate our model, we perform extensive ray-tracing simulations and show that our model is in a very good agreement with the statistical channel properties from ray-tracing. Following hypothesis testing over obtained ray-tracing statistics, we are able to parametrize our model for various 3GPP scenarios under LOS and NLOS propagation conditions. Finally, complementary aspects such as simulation complexity are discussed and a guideline on model implementation is provided.