Conditionally automated driving systems perform all driving tasks under limited conditions, but still request a person to take over in planned situations, such as approaching a highway exit. Previous studies have indicated that the two-stage transition procedure can reduce potential risk during the planned transition. In the two-stage transition procedure, the driver first prepares for the takeover, which is only implemented after the driver is ready. However, when the drivers should begin to prepare for the takeover, was uncertain. Although initiating a preparation request early affords more preparation time, it places greater strain on the driver. This study examined the effects of a two-stage transition procedure with preparation times of 5, 10, 20, and 55 s. The results indicated that the takeover reaction time improved when the preparation time was relatively short (5, 10, or 20 s); however, this insufficiently improved the post-transition driving performance. By contrast, with a relatively long preparation time (55 s), both the takeover reaction time and post-transition driving performance notably improved. Additionally, gaze analysis indicated that drivers were subjected to time pressure and hurried during short preparation periods. These results confirm that a two-stage transition would be more effective when initiated earlier with more preparation time.