Context. Unbiased spectral surveys are powerful tools to study the chemistry and the physics of star forming regions, because they can provide a complete census of the molecular content and the observed lines probe the physical structure of the source. Aims. While unbiased surveys at the millimeter and sub-millimeter wavelengths observable from ground-based telescopes have previously been performed towards several high mass protostars, very little exists on low mass protostars, which are believed to resemble our own Sun's progenitor. To help fill up this gap in our understanding, we carried out a complete spectral survey of the bands at 3, 2, 1, and 0.9 mm towards the solar type protostar IRAS 16293-2422. Methods. The observations covered a range of about 200 GHz and were obtained with the IRAM-30 m and JCMT-15 m telescopes during about 300 h of observations. Particular attention was devoted to the inter-calibration of the acquired spectra with previous observations. All the lines detected with more than 3σ confidence-interval certainty and free from obvious blending effects were fitted with Gaussians to estimate their basic kinematic properties. Results. More than 4000 lines were detected (with σ ≥ 3) and identified, yielding a line density of approximatively 20 lines per GHz, comparable to previous surveys in massive hot cores. The vast majority (about two-thirds) of the lines are weak and produced by complex organic molecules. The analysis of the profiles of more than 1000 lines belonging to 70 species firmly establishes the presence of two distinct velocity components associated with the two objects, A and B, forming the IRAS 16293-2422 binary system. In the source A, the line widths of several species increase with the upper level energy of the transition, a behavior compatible with gas infalling towards a ∼1 M object. The source B, which does not show this effect, might have a much lower central mass of ∼0.1 M . The difference in the rest velocities of both objects is consistent with the hypothesis that the source B rotates around the source A. Conclusions. This spectral survey, although obtained with single-dish telescopes at a low spatial resolution, allows us to separate the emission from two different components, thanks to the large number of lines detected. The data of the survey are public and can be retrieved on the TIMASSS web site .