<p>Scalable implementation of quantum networks and photonic processors demands integrated photonic memories with high efficiency, yet current integrated systems have been limited to storage efficiencies below 27.8%. Here we demonstrate highly efficient integrated quantum memories based on rare-earth-ion-doped crystals coupled with impedance-matched microcavities, realized in two novel architectures: 200-μm-thin membranes of Eu³⁺:Y₂SiO₅ integrated with fibre-based microcavities and waveguide-based cavities fabricated using femtosecond lasers. Our approach achieves reliable integrated quantum storage with record efficiencies of 80.3(7)% for weak coherent pulses and 69.8(1.6)% for telecom-heralded single photons, alongside the storage of 20 temporal modes with an average efficiency of 51.3(2)%. Moreover, the thin-membrane Eu³⁺:Y₂SiO₅ architecture enables spectrally tunable efficient quantum storage via variable strain, providing a flexible interface for quantum networks. By combining high efficiency, large multimode capacity and tunability, our devices establish a versatile hardware foundation for scalable quantum repeaters and chip-scale photonic processors.</p>