Immersive 360° virtual reality (VR) movies can effectively evoke a wide range of different emotional experiences. To this end, they are increasingly deployed in entertainment, marketing and research. Because emotions influence decisions and behavior, it is important to assess the user's affective appraisal of immersive 360° VR movies. Knowledge of this appraisal can serve to tune media content to achieve the desired emotional responses for a given purpose. To measure the affective appraisal of immersive VR movies, efficient immersive and validated instruments are required that minimally interfere with the VR experience itself. Here we investigated the convergent validity of a new efficient and intuitive graphical (emoji-based) affective self-report tool (the EmojiGrid) for the assessment of valence and arousal induced by videos representing 360° VEs (virtual environments). Thereto, 40 participants rated their emotional response (valence and arousal) to 62 videos from a validated public database of 360° VR movies using an EmojiGrid that was embedded in the VE, while we simultaneously assessed their autonomic physiological arousal through electrodermal activity. The mean affective ratings obtained with the EmojiGrid and those provided with the database (measured with an alternative and validated instrument) show excellent agreement for valence and good agreement for arousal. The mean arousal ratings obtained with the EmojiGrid also correlate strongly with autonomic physiological arousal. Thus, the EmojiGrid appears to be a valid and immersive affective self-report tool for measuring VE-induced emotions.