The demand of Virtual Reality (VR) video streaming to mobile devices is booming, as VR becomes accessible to the general public. However, the variability of conditions of mobile networks affects the perception of this type of high-bandwidth-demanding services in unexpected ways. In this situation, there is a need for novel performance assessment models fit to the new VR applications. In this paper, we present PERCEIVE, a two-stage method for predicting the perceived quality of adaptive VR videos when streamed through mobile networks. By means of machine learning techniques, our approach is able to first predict adaptive VR video playout performance, using network Quality of Service (QoS) indicators as predictors. In a second stage, it employs the predicted VR video playout performance metrics to model and estimate end-user perceived quality. The evaluation of PERCEIVE has been performed considering a real-world environment, in which VR videos are streamed while subjected to LTE/4G network condition. The accuracy of PERCEIVE has been assessed by means of the residual error between predicted and measured values. Our approach predicts the different performance metrics of the VR playout with an average prediction error lower than 3.7% and estimates the perceived quality with a prediction error lower than 4% for over 90% of all the tested cases. Moreover, it allows us to pinpoint the QoS conditions that affect adaptive VR streaming services the most.