Context. Dimethyl sulfide, CH3SCH3 (DMS), is a nonrigid, sulfur-containing molecule whose astronomical detection is considered to be possible in the interstellar medium. Very accurate spectroscopic constants were obtained by a laboratory analysis of rotational microwave and millimeter wave spectra, as well as rotation-torsional far-infrared (FIR) spectra, which can be used to predict transition frequencies for a detection in interstellar sources. Aims. This work aims at the experimental study and theoretical analysis of the ground torsional state and ground torsional band ν15 of DMS in a large spectral range for astrophysical use. Methods. The microwave spectrum was measured in the frequency range 2−40 GHz using two Molecular Beam Fourier Transform MicroWave (MB-FTMW) spectrometers in Aachen, Germany. The millimeter spectrum was recorded in the 50−110 GHz range. The FIR spectrum was measured for the first time at high resolution using the FT spectrometer and the newly built cryogenic cell at the French synchrotron SOLEIL. Results. DMS has two equivalent methyl internal rotors with a barrier height of about 730 cm−1. We performed a fit, using the XIAM and BELGI-Cs-2Tops codes, that contained the new measurements and previous transitions reported in the literature for the ground torsional state νt = 0 (including the four torsional species AA, AE, EA and EE) and for the ground torsional band ν15 = 1 ← 0 (including only the AA species). In the microwave region, we analyzed 584 transitions with J ≤ 30 of the ground torsional state νt = 0 and 18 transitions with J ≤ 5 of the first excited torsional state νt = 1. In the FIR range, 578 transitions belonging to the torsional band ν15 = 1 ← 0 with J ≤ 27 were assigned. Totally, 1180 transitions were included in a global fit with 21 accurately determined parameters. These parameters can be used to produce a reliable line-list for an astrophysical detection of DMS.