We present a stochastic model of a sensor-based degradation signal for predicting, in real time, the residual lifetime of individual components subjected to a time-varying environment. We consider future environmental profiles that evolve in a deterministic manner. Unique to our model is the union of historical data with real time sensor-based data to update the degradation model and the residual life distribution (RLD) of the component within a Bayesian framework. The performance of our model is evaluated based on degradation signals from both numerical experiments and a case study using real bearing data. The results show that our approach provides more accurate estimates of the RLD, compared with benchmark models.