We study the optical properties of tetravalent-vanadium impurities in 4H silicon carbide. Light emission from two crystalline sites is observed at wavelengths of 1.28 and 1.33 mu m, with optical lifetimes of 163 and 43 ns, respectively, which remains stable up to 50 and 20 K, respectively. Moreover, spectrally broad photoluminescence is observed up to room temperature. Group-theory and ab initio density-functional supercell calculations enable unequivocal site assignment and shed light on the spectral features of the defects. Specifically, our numerical simulations indicate that the site assignment is reversed with respect to previous assumptions. Our calculations show that vanadium in silicon carbide has highly favorable properties for the generation of single photons in the telecommunication wavelength regime. Combined with the available electronic and nuclear degrees of freedom, vanadium presents all the ingredients required for a highly efficient spin-photon interface.