Cell motility is critical to biological processes from wound healing to cancer metastasis to embryonic development. The involvement of organelles in cell motility is well established, but the role of organelle positional reorganization in cell motility remains poorly understood. Here we present an automated image analysis technique for tracking the shape and motion of Golgi bodies and cell nuclei. We quantify the relationship between nuclear orientation and the orientation of the Golgi body relative to the nucleus before, during, and after exposure of mouse fibroblasts to a controlled change in cell substrate topography, from flat to wrinkles, designed to trigger polarized motility. We find that the cells alter their mean nuclei orientation, in terms of the nuclear major axis, to increasingly align with the wrinkle direction once the wrinkles form on the substrate surface. This change in alignment occurs within 8 hours of completion of the topographical transition. In contrast, the position of the Golgi body relative to the nucleus remains aligned with the pre-programmed wrinkle direction, regardless of whether it has been fully established. These findings indicate that intracellular positioning of the Golgi body precedes nuclear reorientation during mouse fibroblast directed migration on patterned substrates. We further show that both processes are Rho-associated kinase (ROCK) mediated as they are abolished by pharmacologic ROCK inhibition whereas mouse fibroblast motility is unaffected. The automated image analysis technique introduced could be broadly employed in the study of polarization and other cellular processes in diverse cell types and micro-environments. In addition, having found that the nuclei Golgi vector may be a more sensitive indicator of substrate features than the nuclei orientation, we anticipate the nuclei Golgi vector to be a useful metric for researchers studying the dynamics of cell polarity in response to different micro-environments.