The magnetic properties of carbon materials are at present the focus of intense research effort in physics, chemistry and materials science due to their potential applications in spintronics and quantum computing. Although the presence of spins in open-shell nanographenes has recently been confirmed, the ability to control magnetic coupling sign has remained elusive but highly desirable. Here, we demonstrate an effective approach of engineering magnetic ground states in atomically precise open-shell bipartite/nonbipartite nanographenes using combined scanning probe techniques and mean-field Hubbard model calculations. The magnetic coupling sign between two spins was controlled via breaking bipartite lattice symmetry of nanographenes. In addition, the exchange-interaction strength between two spins has been widely tuned by finely tailoring their spin density overlap, realizing a large exchange-interaction strength of 42 meV. Our demonstrated method provides ample opportunities for designer above-room-temperature magnetic phases and functionalities in graphene nanomaterials.