The rotationally resolved infrared spectrum of the B+-D2 ion-neutral complex is recorded in the D-D stretch vibration region (2805–2875 cm−1) by detecting B+ photofragments. Analysis of the spectrum confirms a T-shaped equilibrium geometry for the B+-D2 complex with a vibrationally averaged intermolecular bond length of 2.247 Å, around 0.02 Å shorter than for the previously characterised B+-H2 complex [V. Dryza, B. L. J. Poad, and E. J. Bieske, J. Am. Chem. Soc. 130, 12986 (2008)10.1021/ja8018302]. The D-D stretch band centre occurs at 2839.76 ± 0.10 cm−1, representing a −153.8 cm−1 shift from the Q1(0) transition of the free D2 molecule. A new three dimensional ab initio potential energy surface for the B++H2 interaction is calculated using the coupled cluster RCCSD(T) method and is used in variational calculations for the rovibrational energies of B+-H2 and B+-D2. The calculations predict dissociation energies of 1254 cm−1 for B+-H2 with respect to the B++H2 (j = 0) limit, and 1313 cm−1 for B+-D2 with respect to the B++D2 (j = 0) limit. The theoretical approach reproduces the rotational and centrifugal constants of the B+-H2 and B+-D2 complexes to within 3%, and the magnitude of the contraction of the intermolecular bond accompanying excitation of the H2 or D2 sub-unit, but underestimates the H-H and D-D vibrational band shifts by 7%–8%. Combining the theoretical and experimental results allows a new, more accurate estimation for the B+-H2 band origin (3939.64 ± 0.10 cm−1).