Morphogen gradients instruct cells to pattern tissues. Although the mechanisms by which morphogens transduce chemical signals have been extensively studied, the roles and regulation of the physical communication between morphogen-receiver cells remain unclear. Here, we show that the Wnt/β-catenin-morphogen gradient, which patterns the embryonic anterior-posterior (AP) axis, generates intercellular tension gradients along the AP axis by controlling membrane cadherin levels in zebrafish embryos. This "mechano-gradient" is used for the cell competition-driven correction of noisy morphogen gradients. Naturally and artificially generated unfit cells, producing noisy Wnt/β-catenin gradients, induce local deformation of the mechano-gradients that activate mechanosensitive calcium channels in the neighboring fit cells, which then secrete annexin A1a to kill unfit cells. Thus, chemo-mechanical interconversion-mediated competitive communication between the morphogen-receiver cells ensures precise tissue patterning.