The ferroelectric properties of anisotropically strained SrTiO3 films are analyzed by detailed measurements of the complex dielectric constant as function of temperature, frequency, bias voltage, and electric field direction. At low temperatures, strain induces a relaxor-ferroelectric phase that persists up to room temperature. The transition temperature and characteristic parameters (e.g., Curie temperature, static freezing temperature, degree of diffuseness of the phase transition, activation energy) of the relaxor phase depend strongly on the orientation of the electric field and, therefore, on the amount of structural strain in the given electric field direction. Also above the ferroelectric transition temperature, a relaxation of the permittivity is visible, i.e., the strain causes a relaxor-paraelectric behavior. Only at high enough temperatures, the relaxation time constant tends to zero and the “classical” dielectric state is obtained. Frequency and time dependent relaxation experiments demonstrate an extremely large distribution of the relaxation rates in both relaxor states (ferroelectric and paraelectric), which is indicative for the large distribution in the mobility of polar SrTiO3 regions with randomly distributed directions of dipole moments in the film. The large distribution might be taken as an indication for a large distribution in size and orientation of nanosize domains in the anisotropically strained SrTiO3 film.