Aims. We present the first orbital solution for the O-type supergiant star HD 74194, which is the optical counterpart of the supergiant fast X-ray transient IGR J08408-4503. Methods. We measured the radial velocities in the optical spectrum of HD 74194, and we determined the orbital solution for the first time. We also analysed the complex Hα profile. Results. HD 74194 is a binary system composed of an O-type supergiant and a compact object in a short-period ($P=9.5436\pm0.0002$ d) and high-eccentricity ($e=0.63\pm0.03$) orbit. The equivalent width of the Hα line is not modulated entirely with the orbital period, but seems to vary in a superorbital period ($P=285\pm10$ d) nearly 30 times longer than the orbital one.

4 pages, 6 figures, accepted for publication in A&A