Organic-inorganic atomically precise nanoclusters provide indispensable building blocks for establishing structure-property links in hybrid condensed matter. However, robust glasses of ligand-protected nanocluster solids have yet to be demonstrated. Herein, we show [Cu4I4(PR3)4] cubane nanoclusters coordinated by phosphine ligands (PR3) form robust melt-quenched glasses in air with reversible crystal-liquid-glass transitions. Protective phosphine ligands critically influence the glass formation mechanism, modulating the glasses' physical properties. A hybrid glass utilizing ethyldiphenylphosphine-based nanoclusters, [Cu4I4(PPh2Et)4], exhibits superb optical properties, including >90% transmission in both visible and near-infrared wavelengths, negligible self-absorption, near-unity quantum yield, and high light yield. Experimental and theoretical analyses demonstrate the structural integrity of the [Cu4I4(PPh2Et)4] nanocluster, i.e., iodine-bridged tetranuclear cubane, has been fully preserved in the glass state. The strong internanocluster CH-π interactions found in the [Cu4I4(PPh2Et)4] glass and subsequently reduced structural vibration account for its enhanced luminescence properties. Moreover, this highly transparent glass enables performant X-ray imaging and low-loss waveguiding in fibers drawn above the glass transition. The discovery of "nanocluster glass" opens avenues for unraveling glass formation mechanisms and designing novel luminescent glasses of well-defined building blocks for advanced photonics.