360° video is attracting an increasing amount of attention in the context of Virtual Reality (VR). Owing to its very high-resolution requirements, existing professional streaming services for 360° video suffer from severe drawbacks. This paper introduces a novel end-to-end streaming system from encoding to displaying, to transmit 8K resolution 360° video and to provide an enhanced VR experience using Head Mounted Displays (HMDs). The main contributions of the proposed system are about tiling, integration of the MPEG-Dynamic Adaptive Streaming over HTTP (DASH) standard, and viewport-aware bitrate level selection. Tiling and adaptive streaming enable the proposed system to deliver very high-resolution 360° video at good visual quality. Further, the proposed viewport-aware bitrate assignment selects an optimum DASH representation for each tile in a viewport-aware manner. The quality performance of the proposed system is verified in simulations with varying network bandwidth using realistic view trajectories recorded from user experiments. Our results show that the proposed streaming system compares favorably compared to existing methods in terms of PSNR and SSIM inside the viewport.