A unified system model combining target detection and parameter estimation is established by introducing a target existence state variable. The strict definition of radar information， detection information and spatial information of target is given， and it is proved that the radar information is sum of the detection information and the spatial information of known of target states， which theoretically solves the quantitative problem of the detection information and detection information. We derive the theoretical formula of detection information under the condition of target matching and non-matching， propose a random target detection method， and prove the target detection theorem. The target detection theorem shows that the detection information is achievable， otherwise the empirical detection information of any detector is not greater than the detection information. The target detection information theory proposed in this paper breaks the dominance of the Neyman-Pearson criterion and opens up a new direction for the system theory and design method of target detection.