Using a sample of $771.6 times 10^{6}$ $Upsilon(4S)$ decays collected by the Belle experiment at the KEKB $e^+e^-$ collider, we observe for the first time the transition $Upsilon(4S) to eta h_b(1P)$ with the branching fraction ${cal B}[Upsilon(4S) to eta h_b(1P)]= (2.18 pm 0.11 pm 0.18) times 10^{-3}$ and we measure the $h_b(1P)$ mass $M_{h_{b}(1P)} = (9899.3 pm 0.4 pm 1.0)$ MeV/$c^{2}$, corresponding to the hyperfine splitting $Delta M_{mathrm HF}(1P) = (0.6 pm 0.4 pm 1.0)$ MeV/$c^{2}$. Using the transition $h_b(1P) to gamma eta_b(1S)$, we measure the $eta_b(1S)$ mass $M_{eta_{b}(1S)} = (9400.7 pm 1.7 pm 1.6)$ MeV/$c^{2}$, corresponding to $Delta M_{mathrm HF}(1S) = (59.6 pm 1.7 pm 1.6)$ MeV/$c^{2}$, the $eta_b(1S)$ width $Gamma_{eta_{b}(1S)} = (8 ^{+6}_{-5} pm 5)$ MeV/$c^{2}$ and the branching fraction ${cal B}[h_b(1P) to gamma eta_b(1S)]= (56 pm 8 pm 4) %$.
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