The theory for the calculation of vibronic absorption spectra within a Jahn-Teller (JT) active electronic state from first principles has been developed. The infrared absorption spectra of the 5E' ground state, the low-lying 5E″ excited state of MnF3, and the 4E' state of NiF3 have been computed and analyzed. Dipole moment derivatives have been determined by a linear-plus-quadratic expansion of nuclear dipole moment functions in the JT-active coordinates. Electronic transition dipole moments have been taken into account in the Condon approximation in the diabatic representation. The initial and final vibronic states have been expanded in a product of diabatic electronic states and vibrational basis functions. The effect of spin-orbit coupling on the vibronic infrared spectra of these molecules in their JT-active electronic states has been investigated, by employing the Breit-Pauli spin-orbit operator. The effect of temperature on the vibronic infrared spectra has also been explored. These results represent the first theoretical study of vibronic infrared spectra of JT-active states in transition metal compounds.