Precise geolocalization is crucial for unmanned aerial vehicles (UAVs). However, most current deployed UAVs rely on the global navigation satellite systems (GNSS) or high precision inertial navigation systems (INS) for geolocalization. In this paper, we propose to use a lightweight visual-inertial system with a 2D georeference map to obtain accurate and consecutive geodetic positions for UAVs. The proposed system firstly integrates a micro inertial measurement unit (MIMU) and a monocular camera as odometry to consecutively estimate the navigation states and reconstruct the 3D position of the observed visual features in the local world frame. To obtain the geolocation, the visual features tracked by the odometry are further registered to the 2D georeferenced map. While most conventional methods perform image-level aerial image registration, we propose to align the reconstructed points to the map points in the geodetic frame; this helps to filter out the large portion of outliers and decouples the negative effects from the horizontal angles. The registered points are then used to relocalize the vehicle in the geodetic frame. Finally, a pose graph is deployed to fuse the geolocation from the aerial image registration and the local navigation result from the visual-inertial odometry (VIO) to achieve consecutive and drift-free geolocalization performance. We have validated the proposed method by installing the sensors to a UAV body rigidly and have conducted two flights in different environments with unknown initials. The results show that the proposed method can achieve less than 4m position error in flight at 100m high and less than 9m position error in flight about 300m high.