Ce₂Te₅ is a layered f-electron van der Waals magnet in which reduced dimensionality and inequivalent Ce sites give rise to competing magnetic interactions. We investigate its magnetic ground state using muon spin relaxation (μSR), neutron powder diffraction (NPD), and inelastic neutron scattering (INS). Zero-field μSR reveals an onset of static magnetism below T_C = 5.0(1)~K, followed by an additional anomaly in the internal field at T₂ = 2.3(2)~K, consistent with features observed in bulk thermodynamic and transport measurements. In contrast, NPD data collected between 0.05-8~K reveal a single long-range ordered magnetic phase below T_C, with the magnetic Bragg intensities vanishing at T_C with no evidence for additional structural or magnetic phase transitions down to base temperature. The ordered state is characterized by a commensurate propagation vector k=(0,0,0) and ferromagnetic alignment of Ce moments along the crystallographic b axis. Remarkably, only one of the two crystallographically distinct Ce sites carries an ordered moment of ∼ 0.85(3) μ_B per Ce at 0.05 K. INS measurements establish the crystal electric field (CEF) energy scale of Ce³⁺, revealing low-lying excitations at 7.94 and 21.46 meV and a Kramers doublet ground state with strong single-ion anisotropy. These results demonstrate that Ce₂Te₅ undergoes a single symmetry-breaking magnetic transition, while additional low-temperature anomalies reflect subtle modifications of the ordered state driven by competing interactions and CEF effects.