Low-dimensional quantum materials that remain strongly ferromagnetic down to monolayer thickness are highly desired for spintronic applications. Although oxide materials are important candidates for next generation of spintronics, ferromagnetism decays severely when the thickness is scaled to the nanometer regime, leading to deterioration of device performance. Here we report a methodology for maintaining strong ferromagnetism in insulating LaCoO3 (LCO) layers down to the thickness of a single unit cell. We find that the magnetic and electronic states of LCO are linked intimately to the structural parameters of adjacent "breathing lattice" SrCuO2 (SCO). As the dimensionality of SCO is reduced, the lattice constant elongates over 10% along the growth direction, leading to a significant distortion of the CoO6 octahedra, and promoting a higher spin state and long-range spin ordering. For atomically thin LCO layers, we observe surprisingly large magnetic moment (0.5 μB/Co) and Curie temperature (75 K), values larger than previously reported for any monolayer oxide. Our results demonstrate a strategy for creating ultrathin ferromagnetic oxides by exploiting atomic heterointerface engineering, confinement-driven structural transformation, and spin-lattice entanglement in strongly correlated materials.