The high-dimensional basis of orbital angular momentum (OAM) has several added and unique advantages for photonic quantum technologies compared to the polarization basis, which is only two-dimensional. However, one of the major roadblocks in implementing OAM-based applications with their full potentials is the absence of an ideal OAM-mode detector. Despite the plethora of efforts in the last three decades, currently, there is no OAM detector that can detect a broad OAM-mode spectrum, has uniform detection-efficiency over all the modes, measures the true spectrum, and works for an arbitrary quantum state without the need for any previous information. Here, we experimentally demonstrate just such an OAM detector. We report detection of pure and mixed OAM states with fidelities more than 98% and with measurement times of only a few minutes for dimensionalities up to 100. We expect our work to substantially boost the OAM-based photonic quantum technology efforts.