Excited states in ^{10}B were populated with the ^{10}B(p,p^{'}γ)^{10}B^{*} reaction at 8.5 MeV and their γ decay was investigated via coincidence γ-ray spectroscopy. The emitted γ rays were measured using large-volume LaBr_{3}:Ce and CeBr_{3} detectors placed in anti-Compton shields. This allowed the observation of weak γ-ray transitions, such as the M3 transition between the J^{π},T=0^{+},1 isobaric analog state (IAS) and the J^{π},T=3^{+},0 ground state and the E2 transition between the J^{π},T=2_{1}^{+},0 state and the IAS, i.e., performing measurements of branching ratios at the level of λ≥10^{-4}. For the first time in ^{10}B, the competing M1 and M3 transitions from the decay of the IAS have been observed in a γ spectroscopy experiment. The experimental results are compared with ab initio no-core shell model calculation using the newest version of the local position-space chiral N^{3}LO nucleon-nucleon interaction. The calculations reproduce correctly the ordering of the bound states in ^{10}B, and are in reasonable agreement with the observed branching ratios and reduced transition probabilities.