Local energy extrema of the bands in momentum space, or valleys, can endow electrons in solids with pseudospin in addition to real spin1,2,3,4,5. In transition metal dichalcogenides this valley pseudospin, like real spin, is associated with a magnetic moment1,6 that underlies the valley-dependent circular dichroism6 that allows optical generation of valley polarization7,8,9, intervalley quantum coherence10 and the valley Hall effect11. However, magnetic manipulation of valley pseudospin via this magnetic moment12,13, analogous to what is possible with real spin, has not been shown before. Here we report observation of the valley Zeeman splitting and magnetic tuning of polarization and coherence of the excitonic valley pseudospin, by performing polarization-resolved magneto-photoluminescence on monolayer WSe2. Our measurements reveal both the atomic orbital and lattice contributions to the valley orbital magnetic moment; demonstrate the deviation of the band edges in the valleys from an exact massive Dirac fermion model; and reveal a striking difference between the magnetic responses of neutral and charged valley excitons that is explained by renormalization of the excitonic spectrum due to strong exchange interactions.