Thin films of the archetypal multiferroic TbMnO3 were epitaxially deposited on (0 0 1)-oriented SrTiO3 substrates by means of DC magnetron sputtering. A substrate temperature of 1053 K and an oxygen pressure of 300 Pa were determined to be appropriate growing conditions for obtaining high-quality, epitaxial TbMnO3 films using this physical growing technique. The structural and magnetic properties of ~100 nm thin TbMnO3 films were investigated. X-ray diffraction patterns showed that the films are single-phase and (00ℓ)-oriented. Rocking curves of the (0 0 2) peak confirm the good crystalline quality of the films. X-ray photoelectron spectroscopy analysis confirmed that the nominal valence of the Mn ions is 3+. The films grown on the SrTiO3 substrates displayed substantial epitaxial strain, which decidedly changed the magnetic ground state of the bulk-like counterpart. In particular, the films displayed ferromagnetic-like interactions below a temperature close to the magnetic ordering temperature of the Mn3+ spins (TN ≈ 42 K). Well-defined hysteresis loops with coercive fields as high as 0.1 T were observed at 5 K. The variation of the coercive field with the temperature clearly indicated the presence of low-temperature ferromagnetism in the TMO films. The origin of the anomalous ferromagnetism in the films is discussed in terms of the strain-induced distortion generated by the lattice mismatch between the film and substrate. The reported results can give insight into accurate strategies for controlling single-phase spin-driven multiferroic states.