Heatmap is one of the most popular visualizations of gaze behavior, however, increasingly voluminous streams of eye-tracking data make processing of such visualization computationally demanding. Because of high requirements on a single processing machine, real-time visualizations from multiple users are unfeasible if rendered locally. We designed a framework that collects data from multiple eye-trackers regardless of their physical location, analyses these streams, and renders heatmaps in real-time. We propose a cloud computing architecture (EyeCloud) consisting of master and slave nodes on a cloud cluster, and a web interface for fast computation and effective aggregation of the large volumes of eye-tracking data. In experimental studies of the feasibility and effectiveness, we built a cloud cluster on a well-known service, implemented the architecture and reported on a comparison between the proposed system and traditional local processing. The results showed efficiency of the EyeCloud when recordings vary in durations. To our knowledge, this is the first solution to implement cloud computing for gaze visualization.