Polymorph engineering, defined as the manipulation of material properties through controlled and reversible structural modification, is a promising methodology for inducing useful new properties in 2D materials such as the transition metal dichalcogenides (TMDs). Magnetism is one such property, but polymorph engineering of magnetic TMD monolayers remains unexplored. We have discovered a reversible structural phase transformation in the monolayer TMD material FeSe₂ using scanning tunneling microscopy (STM) that creates new opportunities for polymorph engineering. We find that STM tip-pulsing enables us to electronically convert monolayer FeSe₂ from its ground state in the 1T’-phase to a metastable 1T-phase. The reverse phase transformation from 1T-FeSe₂ to 1T’-FeSe₂ can be achieved thermally. Density-functional theory (DFT) calculations reproduce the observed structural configurations of FeSe₂ and suggest that the 1T'-to-1T structural phase transition is accompanied by a magnetic transition from an antiferromagnetic ground state to a ferromagnetic ground state. Single-layer FeSe₂ is thus a good candidate for magnetic polymorph engineering.