In this paper, a structure and design procedure of a novel double ridged horn antenna with a Gaussian amplitude radiation pattern and stable phase center for two-element direction finding arrays is presented. The radiation properties of the structure are improved through appropriate profiling of the ridge taper and utilization of an elliptical aperture. Furthermore, rigorous numerical optimization is employed to adjust the antenna geometry parameter values. The achieved impedance bandwidth (VSWR < 2) is from 1.5 GHz to 12 GHz (8:1). The antenna exhibits 7 dBi to 20 dBi gain, better than 85% aperture efficiency, > 10 dB side lobe level, as well as low phase center variation (< 5 cm over the operating band). The aforementioned features make the proposed antenna suitable for the amplitude and phase hybrid direction finding applications. The design is validated numerically in CST Microwave Studio.