Ferromagnetic order can be induced in LaCoO3 (LCO) thin films by epitaxial strain. Here, we show that the magnetic properties can be "tuned" by epitaxial strain imposed on LCO thin films by the epitaxial growth on various substrate materials, i.e., (001) oriented SrLaAlO4, LaAlO3, SrLaGaO4, (LaAlO3)(0.3)(Sr2AlTaO6)(0.7), and SrTiO3. The lattice mismatch at room temperature of the in-plane lattice parameters between the substrate, a(s), and bulk LCO, a(b), ranges from -1.31% to +2.63%. Single-phase, < 001 > oriented LCO thin films were grown by pulsed laser deposition on all these substrates. Due to the difference of the thermal-expansion coefficients between LCO and the substrates, the films experience an additional tensile strain of about +0.3% during the cooling process after the deposition at T-s=650 degrees C. The film lattice parameters display an elastic behavior, i.e., an increase of the in-plane film lattice parameter with increasing a(s). From the ratio between the out-of-plane and in-plane strain, we obtain a Poisson ratio of nu approximate to 1/3. All films show a ferromagnetic transition as determined from magnetization measurements. The magnetization increases strongly with increasing tensile strain, whereas the transition temperature T-C after a rapid initial rise appears to saturate at T-C approximate to 85 K above a=3.86 angstrom. The effective magnetic moment mu(eff) in the paramagnetic state increases almost linearly as a function of the mean lattice parameter < a >, indicating an enhanced population of higher spin states, i.e., intermediate- or high-spin states. The experimental results are discussed in terms of a decrease of the octahedral-site rotation with increasing tensile strain.