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Two-dimensional (2D) materials have received a surge in research interest due to their exciting range of properties. Here, we show that 2D cobalt telluride (Co₂Te₃), successfully synthesized via liquid-phase exfoliation in an organic solvent, exhibits weak ferromagnetism behavior at room temperature. Under a small amount of mechanical pressure, the material shows an electrical signal. Here, we also study the effect of the magnetic field on strain generation in the atomically thin Co₂Te₃ material and observe a linear relationship between the output voltage and the applied magnetic field. First-principles density functional theory (DFT) and ab initio molecular dynamics are used to explain these experimental results. Our work could pave the way for the development of 2D materials with coupled magnetism and flexoelectricity, leading to new applications in magnetic field sensing.