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Rubidium atoms on the surface of superfluid helium droplets have been excited into Rydberg states. The excitation spectrum of the Rb-He system has been recorded from the 5$2$D state manifold up to the ionization threshold by resonant three-photon-ionization time-of-flight spectroscopy. The observation of droplet size dependent shifts of excited states with respect to bare atom states is explained by a decreased quantum defect and a lowered ionization threshold. Within the scope of a Rydberg model we demonstrate that quantum defects and ionization thresholds are constant for each specific Rydberg series, which confirms the Rydberg character of excited Rubidium states on helium droplets. A set of six Rydberg series could be identified. Individual Rydberg states are observed with effective principle quantum numbers up to $n\ast \approx 19$ and $l\le 3$, for which the expectation value of the electron orbital radius is about ten times larger than the droplet radius. %.