The decays of the χb1(1P), χb2(1P), χb1(2P) and χb2(2P) mesons into the Υ(1S)μ+μ− final state are observed with a high significance using proton-proton collision data collected with the LHCb detector and corresponding to an integrated luminosity of 9 fb−1. The newly observed decays together with the Υ(2S) → Υ(1S)π+π− and Υ(3S) → Υ(2S)π+π− decay modes are used for precision measurements of the mass and mass splittings for the hidden-beauty states.