Evolution of the capacity to form secondary outgrowths from the principal embryonic axes was a crucial innovation that potentiated the diversification of animal body plans. Precisely how such outgrowths develop in early-branching metazoan species remains poorly understood. Here we demonstrate that three fundamental processes contribute to embryonic tentacle development in the cnidarian Nematostella vectensis. First, a pseudostratified ectodermal placode forms at the oral pole of developing larvae and is transcriptionally patterned into four tentacle buds. Subsequently, Notch signaling-dependent changes in apicobasal epithelial thickness drive elongation of these primordia. In parallel, oriented cell rearrangements revealed by clonal analysis correlate with shaping of the elongating tentacles. Taken together, our results define the mechanism of embryonic appendage development in an early-branching metazoan, and thereby provide a novel foundation for understanding the diversification of body plans during animal evolution.