In perovskite-structure epitaxial films, it has been theoretically predicted that the polarization and the coherence of polar order can increase with increasing crystallographic strain. Experimental evidence of strain-induced long-range ferroelectric order has not been obtained thus far, posing the fundamental question of whether or not strain can induce the long-range polar order. Here we demonstrate the existence of strain-induced ferroelectric order in quantum paraelectric KTaO3 by combining experimental investigations of epitaxial KTaO3 films and density-functional-theory calculations. The long-range ferroelectric order does exist under a large enough epitaxial strain. We suggest that a region of short-range polar order might appear between paraelectric and ferroelectric states in the strain-temperature phase diagrams.