Maneuverability is essential for low Earth orbit (LEO) satellites to fulfill various operational objectives. However, the precise orbit determination (POD) process might deteriorate due to imperfect satellite orbital dynamics modeling. This article develops a generic POD strategy with maneuver handling for LEO satellites equipped with high-performance spaceborne Global Navigation Satellite System (GNSS) receivers. Given the time span of an executed maneuver, a set of constant thrust accelerations in the satellite body-fixed reference frame is estimated without using a-priori maneuver accelerations. In addition, different numbers of velocity pulses are estimated at predefined epochs determined by the duration of a maneuver. POD experiments are done for the GRACE-FO and Sentinel-3 satellites, for which the orbit maneuvers vary significantly. The orbits are assessed via internal consistency checks and external orbit validations. Internally, in each direction, the agreement between the reduced-dynamic and kinematic orbits reaches a level of 1 cm, which is comparable with the reference day without maneuvers. Externally, comparisons with the official GRACE-FO products and orbits from the Sentinel-3 Copernicus POD Quality Working Group confirm the reliability of the new orbits with maneuver handling. Finally, satellite laser ranging and K-band ranging measurements indicate a 1-cm accuracy of the absolute orbits and a 2-mm accuracy of the GRACE-FO relative orbits. The maneuver handling strategy is tested in the Bernese GNSS Software, consistently developed at the Astronomical Institute of the University of Bern.