Magnetic flux leakage (MFL) has been widely applied to the nondestructive testing (NDT) of ferromagnetic materials due to its simple operation, low cost, and steady signal. Its defects are evaluated based on the relationship between MFL signal and the geometrical characteristic of defect. In this paper, a three-dimensional (3D) mathematical model is developed for the magnetic leakage field of surface-breaking defects that are arbitrarily oriented inside ferromagnetic material. Firstly, a finite-length rectangular slot is used as a simplified and convenient representation of a surface-breaking defect. Then, the magnetic charge densities of slot walls in different surface-breaking orientations are analyzed theoretically. The distribution of the magnetic leakage field can ultimately be derived by vector synthesis. Both simulations and experiments are conducted to analyze the magnetic leakage field distributions in different magnetization orientations. The results show that with increasing the angle between the defect orientation and the magnetic field, the horizontal component of the leakage magnetic field increases as demonstrated by increasing the prominence of its single peak. At the same time, however, the vertical component shows a bimodal distribution. The proposed model can effectively describe the influence of defect orientation on MFL signals, which can offer practical guidelines for optimizing MFL detectors and improving defect assessment.