To better cope with significant nonlinear radiation distortions and severe geometric distortions in multisource remote sensing image matching, we propose a high-precision image matching method for multisource remote sensing images based on extended phase consistency (EPC). First, feature detection was performed based on an anisotropic weighted moment equation. We used the EPC model to construct multi-orientation weighted phase sharpness map and the multiscale phase orientation index map and built a gradient location orientation histogram-like local feature descriptor to obtain the corresponding features based on the feature maps. The spatial relationship constraint function was introduced to screen the obtained initial matches to reduce the negative effects caused by the high proportion of outliers. The remaining outliers were removed using the marginalizing sample consensus (MAGSAC) method, and the transformation parameters of the sensed image were calculated based on the iteratively optimized homography matrix model. Based on the feature detection results obtained from two distinct groups of synthetic data, it is evident that the proposed detector outperforms the three classical detectors in terms of repeatability and uniformity. The registration performance experiment data were divided into six groups, and the proposed method was compared with the log-Gabor histogram descriptor, radiation-variation insensitive feature transform, histogram of absolute phase consistency gradients, and local phase sharpness orientation methods. The experimental results showed that the proposed method is significantly better than the existing algorithms in terms of image matching performance and achieves high registration accuracy.