A new methodological approach, based on two innovative reactivity parameters such as the Threshold Alkali Level (TAL) of aggregates and the tolerable driving force (Δtol) provided by an inhibitor of the deleterious alkali-silica reaction (ASR), was used for the assessment of the ASR expansivity of concrete mixes made with different alkali-reactive aggregates and different blended cements (three pozzolanic cements and one blast furnace cement). The alkali-reactivity of the aggregates was also evaluated by using the petrographic examination, the ultra-accelerated mortar bar expansion test in 1M NaOH solution at 80°C and the concrete prism expansion test, the last being performed under two different test conditions (38°C and 100% RH; 60°C and 100% RH). The test results were interpreted according to the innovative methodological approach, as well as according to a traditional approach based on pass-fail criteria. It was found that the reactivity parameters, TAL and Δtol, are appropriate for both qualifying the alkali-reactivity of aggregates and comparing the efficacy of blended cements as ASR inhibitors. These two parameters may be reliably evaluated by using the accelerated (60°C and 100% RH) concrete prism expansion tests.