For the fiber-based magneto-optical (MO) devices, like Faraday optical isolator, the target MO glasses are supposed to strike a balance among the following properties: high Verdet constant, chemical and physical stabilities, compatibility with the fiber drawing process, and the connectivity to the silica glass fiber networks. In this work, we report on the MO application of Tb2O3-Al2O3-SiO2-B2O3 (TASB) glasses as a derivative of the yttrium aluminum silicate (YAS) glass fiber systems which have been intensively studied for their huge potential in the context of all-fiber lasers. We found that MO properties of the obtained TASB glasses vary systematically with the B2O3 contents. The effects of B2O3 on the local glass structures and the valence state of Tb ions were clarified via nuclear magnetic resonance, electron spin resonance, X-ray photoemission spectroscopy, and Raman spectroscopy. B2O3 content in TASB glasses leads to a certain degree of depolymerization in glass network and most of Tb4+ ions from the raw material of Tb4O7 are reduced to Tb3+ ions even in air, resulting in an improved MO properties. Due to the relatively high Verdet constant (similar to 70 rad/T/m) and suitable rheology of the glass melt speculated from the thermal analysis, TASB glass system in this work is adaptable to stable fiber-based Faraday effect devices.