We study both analytically and numerically the edge of two-dimensional ferromagnets with Dzyaloshinskii–Moriya (DM) interactions, considering both chiral magnets and magnets with interface-induced DM interactions. We show that in the field-polarized (FP) ferromagnetic phase magnon states exist which are bound to the edge, and we calculate their spectra within a continuum field theory. Upon lowering an external magnetic field, these bound magnons condense at a finite momentum and the edge becomes locally unstable. Micromagnetic simulations demonstrate that this edge instability triggers the creation of a helical phase which penetrates the FP state within the bulk. A subsequent increase of the magnetic field allows to create skyrmions close to the edge in a controlled manner.