We report vibronically resolved laser-induced fluorescence (LIF) spectra of jet-cooled CS -C10 secondary alkoxy radicals. The LIF spectra demonstrate vibronic structures similar to smaller (C3-C4) secondary alkoxies. For 2-pentoxy and 2-hexoxy, rotationally resolved LIF spectra have also been recorded. Two types of rotational structures have been observed in vibronic bands of each molecule. Extensive quantum chemistry calculations have been performed on 2-pentoxy and 2-hexoxy. The computed results include the relative energies of conformers, their geometries, and the energy separations between the nearly degenerate (A) over tilde and (X) over tilde electronic states (Delta E(A) over tilde-(X) over tilde). Based on the similarity between the vibronic structures of different secondary alkoxies and calculated molecular parameters, including the relative energies of conformers, the (B) over tilde <- (X) over tilde transition frequencies, and the vibrational frequencies, strong vibronic bands in the LIF spectra are assigned to the origin bands and CO stretch bands of the two lowest-energy conformers of each secondary alkoxy radical. The distinct rotational structures of the two different conformations of 2-pentoxy and 2-hexoxy will be simulated and analyzed in Part II of this series (J. Phys. Chem. A 2021, DOI: 10.1021/acs.jpca.0c10663).