We report on the characterization of the X+ 2Σ+ ground and the A+ 2ΠΩ (Ω = 1/2, 3/2) and B+ 2Σ+ electronically excited states of MgXe+. Rotationally cold MgXe in the a 3Π0(v″ = 0) metastable electronic state was generated in a laser-ablation supersonic-beam source. Following single-photon excitation from the metastable state, the vibrational structure of the X+ state of MgXe+ was measured by pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy, and the adiabatic ionization energy of the X+ ← a ionizing transition was determined to be EI/(hc) = 37,468.3(6) cm-1. Spectra of the A+ ← X+ and B+ ← X+ transitions were recorded by using the method of isolated-core Rydberg-dissociation spectroscopy. The observation of the Mg+(3p) 2P1/2 + Xe 1S0 dissociation limit enabled the determination of the dissociation energies of the X+ [D0(X+) = 2970(7) cm-1] and A+ states [D0(A1/2+) = 9781(7) cm-1 and D0(A3/2+) = 9603(7) cm-1]. We compare these results with those of earlier experimental studies and ab initio quantum-chemical calculations.