How long would it take until anesthesia passes (when would he wake up) after a prostatectomy?

5 Minutes. Most patients are awake almost immediately after anesthesia. However, the effects last several hours making the patient's sleepy and groggy. Often patients have no memory of being in recovery room, and this is the lingering effects of the anesthesia. This situation is compounded by the pain medications/narcotics that you will have after the surgery.
Usually very quickly. Most people arouse from anesthesia very quickly, in a matter of a few minutes. In some situations, particularly if the surgery has been long and complicated, they will decide to keep someone sedated for hours after the surgery to give time for the body to stabilize, very old or very sick people may take several hours to recover from the stress of surgery and anesthesia.