Phase transformations in the lithium aluminosilicate glass nucleated by a mixture of yttrium and niobium oxides and doped with cobalt ions were studied for the development of multifunctional transparent glass-ceramics. Initial glass and glass-ceramics obtained by isothermal heat-treatments at 700–900 °C contain YNbO4 nanocrystals with the distorted tetragonal structure. In samples heated at 1000 °C and above, the monoclinic features are observed. High-temperature X-ray diffraction technique clarifies the mechanism of the monoclinic yttrium orthoniobate formation, which occurs not upon high-temperature heat-treatments above 900 °C but at cooling the glass-ceramics after such heat-treatments, when YNbO4 nanocrystals with tetragonal structure undergo the second-order transformation at ~550 °C. Lithium aluminosilicate solid solutions (ss) with β-quartz structure are the main crystalline phase of glass-ceramics prepared in the temperature range of 800–1000 °C. These structural transformations are confirmed by Raman spectroscopy and illustrated by SEM study. The absorption spectrum of the material changes only with crystallization of the β-quartz ss due to entering the Co2+ ions into this phase mainly in octahedral coordination, substituting for Li+ ions. At the crystallization temperature of 1000 °C, the Co2+ coordination in the β-quartz solid solutions changes to tetrahedral one. Transparent glass-ceramics have a thermal expansion coefficient of about 10 × 10−7 K−1.