The passage of time pertains to the dynamic happening of anticipated future events merging into a present actuality and subsequently becoming the past. Philosophers and scientists alike often endorse the view that the passage of time is an illusion. Here we instead account for the phenomenology of time passage as a real psycho-biological phenomenon. We argue that the experience of time passage has a real and measurable basis as it arises from an internal generative model for anticipating upcoming events. The experience of passage is not merely a representation by a passive recipient of sensory stimulation but is generated by predictive processes of the brain and proactive sensorimotor activity of the whole body. Although some philosophical approaches to time consider some psycho-biological evidence, the biological basis of the passage of time has not been examined in detail from a thorough scientific perspective. This paper proposes to remedy this omission.