The invention relates to an omnibearing magnetostatic-field while-drilling positioning method and positioning system for a relief well. The method comprises: (1), a three-axis high-precision flux gate sensor, a three-axis acceleration sensor and a three-axis gyro are installed at a front end of an underground measurement exploring tube; (2), before going down a well, an operator measures a geomagnetic field vector affected by a drill head; (3), after an inclination stage task of a relief well is started, according to magnetic field measurement data obtained by the high-precision flux gate sensor, a measurement while drilling (MWD) exploring tube carries out space projection operation on each group of obtained magnetic field measurement values of a rescued well casing tube by combining attitude information of the MWD, thereby obtaining magnetic field component strength data of the magnetic field of the rescued well casing tube on a horizontal plane in a drilling direction and a direction perpendicular to the drilling direction; (4), least square operation is carried out on the obtained magnetic field component strength data of the rescued well casing tube after space projection of multiple times, thereby obtaining a spatial position of the drilling exploring tube relative to the rescued well casing tube; and (5), filter operation is carried out by a Kalman filter, so that a precise spatial position of a relief well exploring tube relative to the rescued well is obtained.