Counting grape berries and measuring their size can provide accurate data for robot picking behavior decision-making, yield estimation, and quality evaluation. When grapes are picked, there is a strong uncertainty in the external environment and the shape of the grapes. Counting grape berries and measuring berry size are challenging tasks. Computer vision has made a huge breakthrough in this field. Although the detection method of grape berries based on 3D point cloud information relies on scanning equipment to estimate the number and yield of grape berries, the detection method is difficult to generalize. Grape berry detection based on 2D images is an effective method to solve this problem. However, it is difficult for traditional algorithms to accurately measure the berry size and other parameters, and there is still the problem of the low robustness of berry counting. In response to the above problems, we propose a grape berry detection method based on edge image processing and geometric morphology. The edge contour search and the corner detection algorithm are introduced to detect the concave point position of the berry edge contour extracted by the Canny algorithm to obtain the best contour segment. To correctly obtain the edge contour information of each berry and reduce the error grouping of contour segments, this paper proposes an algorithm for combining contour segments based on clustering search strategy and rotation direction determination, which realizes the correct reorganization of the segmented contour segments, to achieve an accurate calculation of the number of berries and an accurate measurement of their size. The experimental results prove that our proposed method has an average accuracy of 87.76% for the detection of the concave points of the edge contours of different types of grapes, which can achieve a good edge contour segmentation. The average accuracy of the detection of the number of grapes berries in this paper is 91.42%, which is 4.75% higher than that of the Hough transform. The average error between the measured berry size and the actual berry size is 2.30 mm, and the maximum error is 5.62 mm, which is within a reasonable range. The results prove that the method proposed in this paper is robust enough to detect different types of grape berries.