This study aimed to comprehensively investigate the properties of a binder based on high-calcium fly ash and silica fume with a complex additive consisting of calcium nitrate and magnesium chloride. The strength characteristics, the characteristics of the hydration process, and the phase composition of the hydration products of the binder were investigated. Silica fume was used to suppress the expansion of fly ash during hydration. A complex additive (CA) consisting of Ca(NO3)2 and MgCl2 provided a higher strength of binder than each of these salts separately. When testing a mortar with sand, the CA additive ensured that the strength of the specimens was 43.5% higher than the strength of the mortar with the addition of Ca(NO3)2 and 7.5% higher than the strength of the mortar with the MgCl2 additive. Calcium nitrate greatly accelerated the process of heat release in the first 60 min of binder hydration, and subsequently, conversely, slowed it down. The addition of MgCl2 gave a significantly greater thermal effect than Ca(NO3)2. When the two salts acted together, even a small fraction of magnesium chloride (0.2 of CA) compensated for the retarding effect of calcium nitrate and provided heat release for the binder that was almost as good as that of MgCl2.