How genes shape diverse plant and animal body forms is a key question in biology. Unlike animal cells, plant cells are confined by rigid cell walls, and cell division plane orientation and growth rather than cell movement determine overall body form. The emergence of plants on land coincided with a new capacity to rotate stem cell divisions through multiple planes, and this enabled three-dimensional (3D) forms to arise from ancestral forms constrained to 2D growth. The genes involved in this evolutionary innovation are largely unknown. The evolution of 3D growth is recapitulated during the development of modern mosses when leafy shoots arise from a filamentous (2D) precursor tissue. Here, we show that a conserved, CLAVATA peptide and receptor-like kinase pathway originated with land plants and orients stem cell division planes during the transition from 2D to 3D growth in a moss, Physcomitrella. We find that this newly identified role for CLAVATA in regulating cell division plane orientation is shared between Physcomitrella and Arabidopsis. We report that roles for CLAVATA in regulating cell proliferation and cell fate are also shared and that CLAVATA-like peptides act via conserved receptor components in Physcomitrella. Our results suggest that CLAVATA was a genetic novelty enabling the morphological innovation of 3D growth in land plants.