The use of whole-slide images (WSIs) in pathology entails stringent storage and transmission requirements because of their huge dimensions. Therefore, image compression is an essential tool to enable efficient access to these data. In particular, color transforms are needed to exploit the very high degree of inter-component correlation and obtain competitive compression performance. Even though the state-of-the-art color transforms remove some redundancy, they disregard important details of the compression algorithm applied after the transform. Therefore, their coding performance is not optimal. We propose an optimization method called mosaic optimization for designing irreversible and reversible color transforms simultaneously optimized for any given WSI and the subsequent compression algorithm. Mosaic optimization is designed to attain reasonable computational complexity and enable continuous scanner operation. Exhaustive experimental results indicate that, for JPEG 2000 at identical compression ratios, the optimized transforms yield images more similar to the original than the other state-of-the-art transforms. Specifically, irreversible optimized transforms outperform the Karhunen-Loève Transform in terms of PSNR (up to 1.1 dB), the HDR-VDP-2 visual distortion metric (up to 3.8 dB), and the accuracy of computer-aided nuclei detection tasks (F1 score up to 0.04 higher). In addition, reversible optimized transforms achieve PSNR, HDR-VDP-2, and nuclei detection accuracy gains of up to 0.9 dB, 7.1 dB, and 0.025, respectively, when compared with the reversible color transform in lossy-to-lossless compression regimes.