Delta Orionis is the closest massive multiple stellar system and one of the brightest members of the Orion OB association. The primary (Aa1) is a unique evolved O star. In this work, we applied a two-step disentangling method to a series of spectra in the blue region (430 to 450 nm), and we detected spectral lines of the secondary (Aa2). For the first time, we were able to constrain the orbit of the tertiary (Ab) -- to 55450d or 152yr -- using variable gamma velocities and new speckle interferometric measurements, which have been published in the Washington Double Star Catalogue. In addition, the Gaia DR3 parallax of the faint component (Ca+Cb) constrains the distance of the system to (381+/-8)pc, which is just in the centre of the Orion OB1b association, at (382+/-1)pc. Consequently, we found that the component masses according to the three-body model are 17.8, 8.5, and 8.7 solar masses, for Aa1, Aa2, and Ab, respectively, with the uncertainties of the order of 1 solar mass. We used new photometry from the BRITE satellites together with astrometry, radial velocities, eclipse timings, eclipse duration, spectral line profiles, and spectral energy distribution to refine radiative properties. The components, classified as O9.5 II + B2 V + B0 IV, have radii of 13.1, 4.1, and 12.0 solar radii, which means that Delta Ori A is a pre-mass-transfer object. The frequency of 0.478 cycles per day, known from the Fourier analysis of the residual light curve and X-ray observations, was identified as the rotation frequency of the tertiary. Delta Ori could be related to other bright stars in Orion, in particular, Zeta Ori, which has a similar architecture, or Epsilon Ori, which is a single supergiant, and possibly a post-mass-transfer object.