The rotational spectra of the normal species and four isotopically substituted species of the dimethyl ether-OCS dimer have been measured by Fourier transform microwave spectroscopy, thereby allowing a structural determination of this weak complex. The normal isotopic species rotational constants are A = 4069.4106(23) MHz, B = 1431.7413(7) MHz, and C = 1074.2925(5) MHz, and the experimental dipole moment components are mu(a) = 1.3046(28) D, mu(b) = 0.8134(37) D, with mu(total) = 1.5374(30) D. Rotational constants, dipole moment components, and planar moments are all consistent with a geometry in which the OCS molecule is located in the heavy-atom plane of dimethyl ether, making an (OC)-C-...-S angle of 96.5(2)degrees, and with an (OC)-C-... separation of 2.916(3) Angstrom. Ab initio calculations at the MP2/6-311++G(2d,2p) level reproduce the structure accurately, predicting rotational constants of A = 4065 MHz, B = 1450 MHz, and C = 1083 MHz.