The growing popularity of virtual and augmented reality communications and 360 • video streaming is moving video communication systems into much more dynamic and resource-limited operating settings. The enormous data volume of 360 • videos requires efficient use of network bandwidth to maintain the desired quality of experience for the end user. To this end, we propose a framework for viewport-driven rate optimized 360 • video streaming that integrates the user view navigation pattern and the spatiotemporal rate-distortion characteristics of the 360 • video content to maximize the delivered user quality of experience for the given network/system resources. The framework comprises a methodology for constructing dynamic heat maps that capture the user likelihood of navigating different spatial segments of a 360 • video over time, analysis and characterization of its spatiotemporal rate-distortion characteristics that leverages preprocessed spatial tilling of the 360 • view sphere, and optimization problem formulation that characterizes the delivered user quality of experience given the user navigation patterns, 360 • video encoding decisions, and the available system/network resources. Our experimental results demonstrate the advantages of our framework over the conventional approach of streaming a monolithic uniformly-encoded 360 • video and a state-of-the-art reference method. Considerable video quality of gains of 4-5 dB are demonstrated in the case of two popular 4K 360 • videos.