The recent discovery of intrinsic ferromagnetic order in the atomically thin van der Waals crystal CrXTe_{3} (X=Si, Ge) stimulates intensive studies on the nature of low-dimensional magnetism because the presence of long-range magnetic order in two-dimensional systems with continuous symmetry is strictly prohibited by thermal fluctuations. By combining advanced many-body calculations with angle-resolved photoemission spectroscopy we investigate CrSiTe_{3} single crystals and unveil the pivotal role played by the strong electronic correlations at both high- and low-temperature regimes. Above the Curie temperature (T_{c}), Coulomb repulsion (U) drives the system into a charge transfer insulating phase. In contrast, below T_{c} the crystal field arranges the Cr-3d orbitals such that the ferromagnetic superexchange profits, giving rise to the bulk ferromagnetic ground state with which the electronic correlations compete. The excellent agreement between theory and experiment establishes CrSiTe_{3} as a prototype low-dimensional crystal with the cooperation and interplay of electronic correlation and ferromagnetism.