This article addresses the problem of robust observer design for nonlinear systems with transformed output. We first assume that there exists an observer design for a given nonlinear system. The structure of the system output is often crucial for estimating the system states. Therefore, we consider the problem that arises when the output is only available under a nonlinear transformation (affected by noise). This formulation is especially useful in engineering applications, where nonlinear sensors are frequent. We propose a new interconnected observer that estimates both the unavailable output and the system states, and we establish small-gain type conditions ensuring the asymptotic convergence of the overall error dynamics. To explicit our design parameters, we study the particular cases of state-affine systems up to output injection and systems with additive triangular nonlinearities. Finally, we provide corresponding numerical examples and comparisons with known observers.