Using a 478 pb$^{-1}$ data sample collected with the BESIII detector operating at the BEPCII storage ring at a center-of-mass energy of $sqrt{s}=4.009$ GeV, the production of $e^{+}e^{-}to eta Jpsi$ is observed for the first time with a statistical significance of greater than $10sigma$. The Born cross section is measured to be $(32.1pm 2.8 pm 1.3)$ pb, where the first error is statistical and the second systematic. Assuming the $eta Jpsi$ signal is from a hadronic transition of the $psi(4040)$, the fractional transition rate is determined to be ${cal B}(psi(4040)to eta Jpsi)=(5.2pm 0.5pm 0.2pm 0.5)times 10^{-3}$, where the first, second, and third errors are statistical, systematic, and the uncertainty from the $psi(4040)$ resonant parameters, respectively. The production of $e^{+}e^{-} to pi^0 Jpsi$ is searched for, but no significant signal is observed, and ${cal B}(psi(4040)to pi^0 Jpsi) < 2.8 times 10^{-4}$ is obtained at the 90% confidence level.
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