Temporal consistency and content preservation are the prominent challenges in artistic video style transfer. To address these challenges, we present a technique that utilizes depth data and we demonstrate this on real-world videos from the web, as well as on a standard video dataset of three-dimensional computer-generated content. Our algorithm employs an image-transformation network combined with a depth encoder network for stylizing video sequences. For improved global structure preservation and temporal stability, the depth encoder network encodes ground-truth depth information which is fused into the stylization network. To further enforce temporal coherence, we employ ConvLSTM layers in the encoder, and a loss function based on calculated depth information for the output frames is also used. We show that our approach is capable of producing stylized videos with improved temporal consistency compared to state-of-the-art methods whilst also successfully transferring the artistic style of a target painting.