Fe electrodeposition on Au(111) and Au(100) in BMIBF4 ionic liquid is found to form hitherto unreported shape-ordered nanoscale morphologies of pseudorods and pseudosquare rings, respectively, both composed of grains of 4-7 nm. The manner of growth of the square rings is a ring-on-ring structure with enlarging side length and slightly protruding four corners. The generality of the growth mechanism is verified by the formation of almost exactly the same shape-ordered Fe nanostructures on Pt, i.e., pseudorod structure on Pt(111) and pseudosquare rings Pt(100). These structures are explained within the framework of magnetostatic interactions of spontaneously magnetized grains under crystallographic constraint of the substrate surface, which result in an antiparallel arrangement in magnetization of the grains at pseudorods and magnetic flux closure at the pseudosquare rings. The closed magnetic flux further leads to magnetic field-enhanced growth at the four corners and the outer peripheries of the pseudosquare rings. The observed shape-ordering of the Fe thin film serves as a paradigm of magnetostatic coupling, in which the roles of ionic liquid as surfactant and magnetic media may not be underestimated. The present work adds a new dimension to electrodeposition in ionic liquid, by which new magnetic film structures may be expected.