Efficient integrated quantum memories are a key enabling technology for scalable quantum networks and photonic quantum processors, yet their efficiencies have remained below the critical threshold of 90% required for demanding applications. Here we demonstrate an integrated photonic quantum memory with a storage-and-retrieval efficiency of 90.2(4)% for single-photon-level weak coherent pulses and a storage fidelity of 99.3(1)% for time-bin qubits, using a waveguide cavity fabricated in Pr${}^{3+}$:$Y_{2}Si{O}_5$. This performance is enabled by the high absorption-to-loss ratio of Pr${}^{3+}$ ions in a low-loss waveguide cavity, combined with a time-reversal technique to overcome the dispersion-limited cavity linewidth and a novel spectral preparation scheme that creates a clean transparency window while utilizing a single class of ions that is compatible for spin-wave storage. Our results establish the first integrated photonic memory beyond the 90% efficiency threshold, representing an important step toward applications that demand the highest performance, such as scalable quantum repeaters, photonic quantum computing and device-independent quantum key distribution.