Understanding how an independent organ develops from the stem cell populations in the process called morphogenesis is a pressing challenge in developmental biology and medicine. Plants build up new organs such as roots to adjust their bodies to dynamic changes in the environment, thereby providing a tractable model to address this challenge. Here, we combined empirical data with advanced computer modeling techniques to build a mechanistic cell-based framework for the morphogenesis of the plant root. Our framework relies on experimentally supported design principles underlying the multi-layered feedback between tissue mechanics, cell growth, and directional cell-to-cell transport of growth regulator auxin. Model simulations reconstruct experimentally-observed patterns of anisotropic growth, auxin distribution, and cell polarity, as well as several root phenotypes caused by chemical, mechanical, or genetic perturbations. Furthermore, our model provides new insights into mechanisms of sustained root growth and cell polarity establishment. This work reveals that mobile auxin signal feeds back on cell polarity and growth mechanics to instruct the morphogenesis of an independent organ.