Oxide heterostructures often exhibit unusual physical properties that are absent in the constituent bulk materials. Here, we report an atomically sharp transition to a ferromagnetic phase when polar antiferromagnetic LaMnO3 (001) films are grown on SrTiO3 substrates. For a thickness of six unit cells or more, the LaMnO3 film abruptly becomes ferromagnetic over its entire area, which is visualized by scanning superconducting quantum interference device microscopy. The transition is explained in terms of electronic reconstruction originating from the polar nature of the LaMnO3 (001) films. Our results demonstrate that functionalities can be engineered in oxide films that are only a few atomic layers thick.