The rotational spectrum of the 1: 1 weakly bound complex formed between dimethyl ether (DME) and CO2 has been assigned by Fourier transform microwave spectroscopy, leading to rotational constants of A = 5401.24(11) MHz, B = 2010.8637(17) MHz, and C = 1493.4844(15) MHz for the normal isotopic species. Measurement of rotational spectra for an additional four isotopomers has allowed a structure determination for this complex, giving a C-2v geometry in which the CO2 lies in the heavy atom plane of the DME and is aligned perpendicular to its C-2 axis. This orientation is supported by second moment data and a dipole moment of mu(a) = mu(total) = 1.661(6) D. The (CO)-O-... distance has been determined to be 2.711 (1) Angstrom. Ab initio optimizations at the MP2/6-311++G(2d,2p) level predict a C-2v geometry with a (CO)-O-... bond length of 2.685 Angstrom, slightly shorter than, but still in very good agreement with, the experimental value. Predicted rotational constants and dipole moment at this level of theory are A = 5379 MHz, B = 2018 MHz, C = 1495 MHz, and mu(a) = 1.83 D.